The fundamental period (TFP) of vibration is the time required for a structure to complete one full cycle of vibration, and it is one of the main features of the structural system. It highly influences the behavor of structures under earthquake excitation. Therefore, its determination is of highest importance for the seismic design of buildings. This is a complex task in a case of masonry infilled RC frames, due to high stiffness of infill walls and their interaction with the surrounding frame. In this study, using Artificial Neural Network (ANN) algorithms, the fundamental (natural) period of vibration of fully or partially masonry infilled Reinforced Concrete (RC) frame structures was evaluated. Accurate prediction of TFP has a key role in ensuring the safety and resilience of structures, which is particularly expressed in seismic-prone regions. The collected database from open literature contains 4026 samples which cover a wide range of RC frames. For practical reasons, the database is divided in the preprocessing phase into two parts that contain either bare frames or fully/partially infilled frames. The authors compared first and second-order ANN paradigms, and conducted feature importance analysis. The proposed models were validated and verified by comparison with the experimental data, seismic design codes, and derived equations by other researchers. In addition to the superiority that the BRA model has shown in comparison with other solutions, it also enables simpler approach for the calculation of TFP, unlike the proposals of other authors. Based on the results from best ANN model, multi-objective optimization genetic algorithm was employed for additional optimization of TFP which include investigation of the most optimal solutions between two conflicting objective functions.