This paper introduces the equations of motion of modular 2D snake robots moving in vertical plane employing Series Elastic Actuators (SEAs). The kinematics of such 2D modular snake robot is presented in an efficient matrix form and Euler–Lagrange equations are constructed to model the robot. Moreover, using a spring-damper contact model, external contact forces, necessary for modeling pedal wave motion (undulation in the vertical plane) are taken into account, which unlike existing methods can be used to model the effect of multiple contact points. Using such a contact model, pedal wave motion of the robot is simulated and the torque signal measured by the elastic element from the simulation and experimentation are used to show the validity of the model. Moreover, pedal wave locomotion of such robot on uneven terrain is also modeled and an adaptive controller based on torque feedback in gait parameter's space with optimized control gain is proposed. The simulation and experimentation results showed the efficacy of the proposed controller as the robot successfully climbed over a stair-type obstacle without any prior knowledge about its location with at least 24.8% higher speed compared with non-adaptive motion.