Two models for the motion in the Mataf of the Holy Mosque of Makkah that are applicable to any so-called social force or agent-based model are presented. The first model assigns a desired distance to the Kaaba to each pilgrim. The second model assumes that pilgrims desire to get as close as possible to the Kaaba until a tolerable density is reached. Both models are realistic: image data shows behaviours of both types. The models are very simple to incorporate into any computational crowd dynamics code, and yield results that correlate surprisingly well with observed data.