A unique three-dimensional packing problem with non-convex parts and without a gravity constraint can be defined in a selective laser sintering rapid prototyping machine. The goal for the packing task is to pack the parts to be manufactured as tightly as possible to maximize volume and machine time utilization. A genetic algorithm is used as a search engine to find a good packing pattern for parts. Each individual in a population represents one packing solution. The chromosomal representation is a three-dimensional ordered list of integers where each sublist has a different allele set. A fitness function simulates the packing of parts and also evaluates the quality of a solution. To calculate part intersections, the fitness function uses methods common in computational geometry. Due to the chromosome structure used, there is a lack of genetic material in the population. Methods to introduce new material into the population are defined and tested. Experiments with more difficult packing problems, where all parts are complex in shape, prove that the developed genetic algorithm is robust and able to find a good solution in most problem instances.