Bob said:
Interestingly, the article suggested by Bob I shows that Cisco
recommends that the network admin make it difficult for non-authorized
people with access to the network to find out the make and model of the
router:
"As a general rule, any unnecessary service should be disabled in any
router that is reachable from a potentially hostile network. The
services listed in this section are sometimes useful, but should be
disabled if they are not actively used. ... Cisco Discovery Protocol
(CDP) is used for some network management functions, but is dangerous
because it allows any system on a directly-connected segment to learn
that the router is a Cisco device, and to determine the model number and
the Cisco IOS software version that is run. This information can be used
to design attacks against the router."
If the OP has the necessary credentials to log into the router, he/she
can easily determine the model number that way.