In the design and analysis of optical systems folded by prieme, the conventional method of unfolding the prisms and treating them as glass slabs has its limitations. In many cases (such as in the toleranoing of prism angular errors), surfaoe-by-surface finite ray-traoing is needed. Coordinate transfer formulae required in tracing rays through deoentred and tilted surfaces are derived in a general and simple form. A new method is developed for ray-tracing through roof prisms and corner cube prismswhich have special geometric structures.