Cell migration is a highly regulated and complex cellular process to maintain proper homeostasis for various biological processes. Extracellular environment was identified as the main affecting factors determining the direction of cell crawling. It was observed experimentally that the cell prefers migrating to the area with denser or stiffer array of microposts. In this article, an integrated unidirectional cell crawling model was developed to investigate the spatiotemporal dynamics of unidirectional cell migration, which incorporates the dominating intracellular biochemical processes, biomechanical processes and the properties of extracellular micropost arrays. The interpost spacing and the stiffness of microposts are taken into account, respectively, to study the mechanism of unidirectional cell locomotion and the guidance of extracellular influence cues on the direction of unidirectional cell crawling. The model can explain adequately the unidirectional crawling phenomena observed in experiments such as “spatiotaxis” and “durotaxis,” which allows us to obtain further insights into cell migration.