In seismic design and structural evaluation, understanding the fundamental period (FP) of a building is of paramount importance. It also serves as a pivotal assessment parameter for a structure’s overall response. Different international codes suggest empirical formulations which focus on distinct factors such as the height of Bare Frame Reinforced Concrete (RC) structures to calculate the fundamental period of the building. This paper systematically summarizes the influence of key parameters, encompassing the overall height of the building, the width of individual bays, the total number of bays, and the foundational support conditions considering soil-structure interaction (SSI), on the FP for RC bare frame structures. This paper involves a comprehensive modal analysis of a diverse set of 320 building models, each defined by a specific combination of the parameters mentioned above. This investigation aims to shed light on the interaction of these factors on the fundamental vibration periods. This study also proposes a new equation using multiple linear regression analysis which incorporates the above-mentioned selected parameters to predict the building’s FP. The proposed model exhibits better predictive competence in contrast to the established code equations.