Using the Reduced Differential Transform Method (RDTM), it is possible to find the exact solutions or better approximate solutions of wide classes of problems in mathematical physics. The coupled KdV equations introduced by Hirota-Satsuma and Modified Camassa- Holm equation introduced by Wazwaz have rich applications in mathematical physics. In this paper, this method is used for solving these nonlinear equations with given initial conditions containing arbitrary constants. The numerical solutions obtained by RDTM are compared with the exact known solutions by fixing the arbitrary constants. The obtained results show that the solutions obtained by RDTM are in good agreement with the exact solutions.