Transmission expansion planning (TEP) aims to define the location, timing, and quantity of reinforcements that must be implemented in the power grid. By defining reinforcement strategies, TEP ensures that the transmission infrastructure is prepared to meet increased demand, the integration of new generation sources, and new technologies that emerge in the electricity sector. However, modeling the problem has become more challenging due to the increase in size and complexity of electrical systems. As a consequence, the amount of uncertainties involved requires optimization tools that enable the efficient management of economic resources. Therefore, this dissertation proposes the use of an algorithm named SMC-CE-TEP, which is based on the cross-entropy method with the aid of Monte Carlo simulation, to solve the optimization of the TEP problem. Through a probability distribution, the algorithm is run, and several expansion plans can be identified. To analyze the proposed method, the long-term static TEP problem is solved through a linearized DC network model with the inclusion of ohmic losses and consideration of N-1 security criterion for the transmission network. Two test systems, often used in this research topic, are employed in the validation process of the proposed method.