This work focuses on enhancing step descending ability of the modular robot proposed in [16]. The proposed robot consists of three modules connected with each other through passive joints. It is propelled using an active pair of wheels per module. Since there are no actuators at the joints, the joints are not susceptible to losing operability while traversing on rugged terrain. However with the absence of actuators, we face the issue of the robot toppling over when an abnormally large obstacle is encountered. This shortcoming is overcome with the use of compliant joints. The compliant joints are designed by employing springs of optimal stiffness, which is calculated through an optimization formulation aided with the constraints presented by the static analysis of the robot. The novelty lies in the systematic design of compliant joint for step descent. The robot is successful in climbing and descending obstacles of dimension 17 cm. Simulations of the mathematically modelled robot are carried out. The results from the same are validated on a working prototype and presented. © 2015 ACM.