Curved cylinders, if rigid, cannot roll on a surface like straight cylinders, but soft cylinders bent by specific stimuli can! Studying the autonomous locomotion of these soft robots and their interactions with the environment using finite element analysis is challenging due to the complex multiphysics of stimuli-responsive soft materials and nonlinear contact mechanics. In this pioneering work, we simulate the rolling of stimuli-bent cylinders on a surface using contact finite elements and introduce a simple yet effective pseudo-thermal field method. Our approach successfully reproduces several modes of autonomous locomotion observed experimentally, including phototropic locomotion, phototropic climbing on a slanted surface, steering under partial illumination, and backward rolling under alternating heat-light stimuli. Parametric analysis demonstrates strong agreement between the experiments and our numerical results, validating the effectiveness of our approach. This study reveals the intriguing and highly nonintuitive dynamics of photo- or thermally bent cylindrical soft robots, and serves as a paradigm for modelling and simulating such rolling robots.