This paper describes a new computational scheme to model crystal structures of organic compounds employing a modified genetic algorithm. The method uses real-valued Cartesian coordinates and Euler angles between molecules in a crystal block as variables identifying the genetic parameters, i.e., genes. The model does not make any assumption on the crystallographic group at which the compound belongs nor to the number of molecules in the unit cell. The method has been implemented in the computer package MGAC (Modified Genetic Algorithm for Crystal and Cluster structures) that allows for optimizations using any arbitrary selection function. The examples presented here for the crystalline structures of benzene, naphthalene and anthracene, using an empirical potential energy function as the selection function, show excellent agreement with the experimental ones. While these examples use the "rigid molecule approximation," the method is quite general and can be extended to take into account any number of intramolecular degrees of freedom.