This paper presents an algorithm for the solution of the side chain placement problem.The algorithm combines the application of the Goldstein elimination criterion with the univariate marginal distribution algorithm (UMDA), which stochastically searches the space of possible solutions. The suitability of the algorithm to address the problem is investigated using a set of 425 proteins.For a number of difficult instances where inference algorithms do not converge, it has been shown that UMDA is able to find better structures.The results obtained show that the algorithm can achieve better structures than those obtained with other state-of-the-art methods like inference-based techniques. Additionally, a theoretical and empirical analysis of the computational cost of the algorithm introduced has been presented.