Topology optimization of structures is a discipline that is based on obtaining the optimal distribution of material in a given structural domain under specific loads and boundary conditions. It was in the late 1980s when this type of structural optimization began to gain relevance through articles by researchers like Bendsøe and Kikuchi. The commonly used formulation for topology optimization is minimizing the mean compliance and elastic strain energy with volume constraints. This methodology has so much relevance due to the computational advantages it provides. Nevertheless, some other formulations have been developed the last few decades, such as the minimun weight objective function with stress constraints formulation. Some authors began to work on this idea in order to obtain a mehtodology that would align with the usual procedures in structural optimization, ensuring the structural strength and carrying out effective control of its stresses. The main objective of this work is to continue this line of research by implementing eigenvalues constraints to ensure control over elastic and dynamic stability of the optimal structures. Some works appeared recently following this line too, but using the mean compliance formulation. In conclusion, this work aims to obtain optimal structures within a specific domain, ensuring their proper structural performance and controlling buckling and natural vibration frequencies. Some numerical examples related to civil engineering are stated to validate the methodology.