ABSTRACT The two-dimensional cutting problem has a direct relationship with industry problems. There are several proposals to solve these problems. In particular, solution proposals using metaheuristics are the focus of this research. Thus, in this paper, we present a specialized biased random key genetic algorithm. Several tests were performed using known instances in the specific literature, and the results found by the metaheuristics proposed were, in many cases, equal or superior to the results already published in the literature. Another comparison of results presented in this paper is related to the results obtained by specialized metaheuristics and the results found by a mathematical model using commercial software. Once again, in this case, the genetic algorithm presented results equal to or very close to the optimum found by the mathematical model. In addition, the optimization proposal was extended to two-dimensional non-guillotine cutting without parts orientation.