The average magnetization of thin simple cubic Ising films (with thicknesses n of 1, 2, 3, 5, 10 and 20 atomic layers, respectively) is calculated as a function of temperature using the Monte Carlo technique. The "magnetization profile" across the film is also obtained. To approximate the infinite extension in the plane parallel to the surfaces of the films, films with linear dimensions 55 × 55 and periodic boundary conditions are considered. The shift of the critical temperature is consistent with an n-λ law where λ = 1/v3 = 1.56 is the reciprocal exponent of the correlation length. This result is critically compared with previous estimates obtained by various authors using other techniques. By interpreting the results in terms of Fisher and Barber's scaling theory, the finite size scaling function for the magnetization is determined. It is pointed out that the spatial distribution of the magnetization can be reasonably interpreted in terms of surface properties. © 1974.