The neutron escape probability from a rectangular cell is investigated for the collision probability method. Since the numerical calculation of the escape probability requires multiple integrations, resulting in a long computing time, semianalytical approximation of the multiple integrations is proposed to reduce the computing time. By approximating the result of integration in the z-direction by a polynomial expression divided into ranges, it is possible to perform the integrations in the x- and y-directions analytically. The computing time of the present semianalytical approximation is reduced by one to two orders of magnitude compared with that required for the conventional numerical integration. Moreover, a lookup escape probability table for rectangular cells calculated using the semianalytical approximation enables the calculation of the escape probability for an arbitrary rectangle with a much shorter computing time and practical precision (<0.1% error). In addition, a method of applying the semianalytical approximation and a lookup table to the collision probability calculation for an x-y geometry is discussed.