The paper describes a Fortran IV program for estimation of a non‐linear‐in‐the‐parameters production function known as the Constant Elasticity of Substitution (CES) model (see Arrow et al., 1961). This model, specified with multiplicative errors, is estimated by applying an approximate modified Newton method in which second‐order derivatives are not computed; the method is discussed in connection with the technique used for restraining the parameters in the iterative process and ensuring non‐negative marginal products. The program has been tested for a large number of samples the estimation of which has been shown sufficiently accurate and rapid.