I'm trying to setup a tunnel between two linux servers which are routers for thier individual network. When setting up the tunnel, before adding the route, I am not able to ping the remote server via the Tunnel IP but I am able to via the Internet IP. Iptables have allow rules for all traffic coming from from one server to another for both INPUT and FORWARD tables. Can anyone help? My configurations are below:

Setup the Tunnel
Code:
SERVER X
interface eth0 :: address X.X.X.X on the Internet
interface eth1 :: address 10.1.0.1, network 10.1.0.0/16

ip link set gre0 up
ip tunnel add tun0 mode gre local X.X.X.X remote Y.Y.Y.Y ttl 20 dev eth0
ip addr add dev tun0 10.2.0.1 peer 10.2.0.2/24
ip link set dev tun0 up


SERVER Y
interface eth0 :: address Y.Y.Y.Y on the Internet
interface eth1 :: address 10.0.0.1, network 10.0.0.0/16

ip link set gre0 up
ip tunnel add tun0 mode gre local Y.Y.Y.Y remote X.X.X.X ttl 20 dev eth0
ip addr add dev tun0 10.2.0.2 peer 10.2.0.1/24
ip link set dev tun0 up
Ifconfig
Code:
SERVER X
eth0      Link encap:Ethernet  HWaddr   
          inet addr:X.X.X.X  Bcast:  Mask:255.255.255.248
          UP BROADCAST RUNNING MULTICAST  MTU:1500  Metric:1
          RX packets:49528 errors:0 dropped:0 overruns:0 frame:0
          TX packets:46561 errors:77 dropped:0 overruns:0 carrier:154
          collisions:28 txqueuelen:1000 
          RX bytes:41880714 (41.8 MB)  TX bytes:24502227 (24.5 MB)
          Interrupt:23 Base address:0xdc00 

eth1      Link encap:Ethernet  HWaddr 
          inet addr:10.1.0.1  Bcast:10.1.255.255  Mask:255.255.0.0
          UP BROADCAST RUNNING MULTICAST  MTU:1500  Metric:1
          RX packets:123676 errors:0 dropped:0 overruns:0 frame:0
          TX packets:96316 errors:0 dropped:0 overruns:0 carrier:0
          collisions:0 txqueuelen:1000 
          RX bytes:29359919 (29.3 MB)  TX bytes:45787455 (45.7 MB)
          Interrupt:20 

lo        Link encap:Local Loopback  
          inet addr:127.0.0.1  Mask:255.0.0.0
          UP LOOPBACK RUNNING  MTU:16436  Metric:1
          RX packets:9445 errors:0 dropped:0 overruns:0 frame:0
          TX packets:9445 errors:0 dropped:0 overruns:0 carrier:0
          collisions:0 txqueuelen:0 
          RX bytes:957778 (957.7 KB)  TX bytes:957778 (957.7 KB)

tun0      Link encap:UNSPEC  HWaddr 40-B5-4D-2A-00-00-00-00-00-00-00-00-00-00-00-00  
          inet addr:10.2.0.1  P-t-P:10.2.0.2  Mask:255.255.255.255
          UP POINTOPOINT RUNNING NOARP  MTU:1476  Metric:1
          RX packets:0 errors:0 dropped:0 overruns:0 frame:0
          TX packets:26 errors:0 dropped:0 overruns:0 carrier:0
          collisions:0 txqueuelen:0 
          RX bytes:0 (0.0 B)  TX bytes:2184 (2.1 KB)

SERVER Y
eth0      Link encap:Ethernet  HWaddr 
          inet addr:Y.Y.Y.Y  Bcast:  Mask:255.255.252.0
          UP BROADCAST RUNNING MULTICAST  MTU:1500  Metric:1
          RX packets:262492 errors:0 dropped:0 overruns:0 frame:0
          TX packets:190556 errors:0 dropped:0 overruns:0 carrier:0
          collisions:0 txqueuelen:1000 
          RX bytes:200110162 (200.1 MB)  TX bytes:27142287 (27.1 MB)

eth1      Link encap:Ethernet  HWaddr 
          inet addr:10.0.0.1  Bcast:10.0.255.255  Mask:255.255.0.0
          UP BROADCAST RUNNING MULTICAST  MTU:1500  Metric:1
          RX packets:240479 errors:0 dropped:0 overruns:0 frame:0
          TX packets:447214 errors:0 dropped:0 overruns:0 carrier:0
          collisions:0 txqueuelen:1000 
          RX bytes:33490787 (33.4 MB)  TX bytes:481346489 (481.3 MB)

lo        Link encap:Local Loopback  
          inet addr:127.0.0.1  Mask:255.0.0.0
          UP LOOPBACK RUNNING  MTU:16436  Metric:1
          RX packets:1142 errors:0 dropped:0 overruns:0 frame:0
          TX packets:1142 errors:0 dropped:0 overruns:0 carrier:0
          collisions:0 txqueuelen:0 
          RX bytes:132394 (132.3 KB)  TX bytes:132394 (132.3 KB)

tun0      Link encap:UNSPEC  HWaddr CC-6F-B5-E5-00-00-00-00-00-00-00-00-00-00-00-00  
          inet addr:10.2.0.2  P-t-P:10.2.0.1  Mask:255.255.255.255
          UP POINTOPOINT RUNNING NOARP  MTU:1476  Metric:1
          RX packets:26 errors:0 dropped:0 overruns:0 frame:0
          TX packets:34 errors:0 dropped:0 overruns:0 carrier:0
          collisions:0 txqueuelen:0 
          RX bytes:2184 (2.1 KB)  TX bytes:2856 (2.8 KB)
IpTunnel
Code:
SERVER X
gre0: gre/ip  remote any  local any  ttl inherit  nopmtudisc
tun0: gre/ip  remote Y.Y.Y.Y  local X.X.X.X  dev eth0  ttl 20 

SERVER Y
gre0: gre/ip  remote any  local any  ttl inherit  nopmtudisc
tun0: gre/ip  remote X.X.X.X  local Y.Y.Y.Y  dev eth0  ttl 20