The capacity restrained traffic assignment problem is defined as "assign the vehicular traffic to different links of the network, given an origin-destination matrix for the traffic required between the nodes of the network, and a nonlinear relation for the travel time on each link as function of the traffic flow in that link ". The traffic is assumed to follow user's optimization according to Wardrop's principle, which states that the travel casts on all used pathes for each of the origin-destination pairs are equal and less than the travel cost on the unused pathes. This paper introduces four methods representing different approachs for solving this problem, the successive incremental assignment, Leblanc's model, a modified form of Leblanc's model and the method of negative loops. These methods are explained and compared with the help of an illustrative example.