A direct method for the calculation of the chord length distribution function f(l), for special as well as more general geometries, is investigated here. The method is tested against well-known results for sphere and infinite slab. Then, a derivation of P(x), the escape probability function, for an infinite square prism is presented. This method differs from Carlvik's in that, instead of currents into the surface, f(l) is derived here based on geometrical considerations alone. For P(x) we only assume a homogeneous source in fuel.