A study of dynamics of a waveboard is presented. The equations of motion are derived and analysed to understand the intriguing propulsion mechanism. A reduced order model is obtained, and the contributions of different terms are clearly brought out. The geometry of the castor wheels is found to play a key role in the conversion of the twisting oscillatory motion of the rider to the forward translational motion. The process of periodic gain in potential energy and its subsequent conversion to kinetic energy aids the propulsion. Interestingly, the dynamic analysis reveals that the efficacy of this propulsion mechanism tapers off as the speed increases. Rolling resistance in the wheels ultimately limits the speed of the device. The effect of various geometric and dynamic parameters on the motion and forces are studied, and optimality of design is indicated.