This paper presents the design and manufacture process of a wheel-less, modular snake robot with Series Elastic Actuators to reliably measure motor torque signal and investigate the effectiveness of active stiffness control for achieving adaptive snake-like locomotion. A Polyurethane based elastic element to be attached between the motor and the links at each joint has been designed and manufactured using water jet cutter, which made the final design easier to develop and more cost-effective, compared to existing snake robots with torque measurement capabilities. The reliability of such torque measurement mechanism examined using simulated dynamical model of pedal wave motion, which proved the efficacy of the design. A distributed control system is also designed, which with the help of an admittance controller, enables active control of the joint stiffness to achieve adaptive snake robot pedal wave locomotion to climb over obstacles, which unlike existing methods does not require prior information about the location of the obstacle. The effectiveness of the proposed controller in comparison to open-loop control strategy has been shown by the number of experiments, which showed the capability of the robot to successfully climb over obstacles with the height of more than 55% of the diameter of the snake robot modules.