Genetic algorithms coupled with the least square method are applied to obtain variable through-thickness residual stresses by the ASTM E 835-95 hole drilling method. Assuming the unknown residual stress functions to be represented by a linear combination of elementary base functions, the solution can be obtained by solving integral equations with known analytical kernels. Genetic algorithms were found to be efficient tools for choosing the optimal parameters of the bases which gave the best fit of measured relaxed strain distributions. Some practical applications are discussed.