In this work, the estimation of the fundamental period of vibration of masonry infilled RC frame structures is achieved using both Machine Learning techniques and concise nonlinear formulas. The data used are extracted from a recently published extensive database that associates the period with relevant information, such as the height of the structure, the span length between columns, the wall opening ratio, and the masonry wall stiffness. It is shown that, as compared to the utilized data, the proposed methods produce excellent results at the cost of various levels of complexity.