Biological evolution as conceived by the present synthetic theory of evolution is modelled by a mathematical system which consists of three arrays: the genotype and phenotype population and their environment, and four operators: selection, mutation, recombination, and alteration (describing the change of the environment by the population). An evolutionary process then could be represented as the cyclic iteration of these operations on the respective arrays. Some simple versions of this system were investigated by computer simulation. They exhibited the following properties. (i) Population fitness increased with the generation number. (ii) The evolutionary rate increased with variance of fitness. (iii) The evolutionary rate increased with the number of individuals, and decreased with the number of loci. (iv) The evolutionary rate increased with the selection pressure. (v) For a given system in a given state there existed an optimal mutation rate. (vi) Free recombination was optimal. (vii) The mutational load of fitness increased with the mutation rate, but was independent of the selection pressure; contrary to this, the mutational load of the population “morph” decreased with the selection pressure, i.e. one could compensate for the deleterious effect of mutation by strong selection. These rules applied to haploids with equal, unequal, non-epistatic, and epistatic gene effect, and also to diploids. It was found that epistatic gene effect for relatively low mutation rates slows down evolution, whereas unequal gene effect enhances it. Diploids were not found to be superior to haploids in evolutionary terms, except in the case of diploids with dominant gene action for very small population sizes. The results are discussed with regard to their applicability to the simulation of more complex evolutionary phenomena.