Buildings with reinforced concrete (RC) integrate steel reinforcement with concrete to increase the structure’s durability and load-bearing capability. A significant issue is the corrosion of the steel reinforcement, especially in high-humidity environments or when exposed to deicing salts. This paper proposes a novel technique for predicting the fundamental period (FP) of RC buildings considering infill walls and soil–structure interaction (SSI) effects. The proposed technique is the multi-component attention graph convolutional neural network (MCAGCNN). The primary objective of the proposed method is to achieve high prediction accuracy and minimal error in approximating the FP of RC frame-building models, thereby improving the reliability of structural analysis and design. Initially, data are collected from Housing Database Project Level Files. This study primarily investigated three types of buildings: Bare frames, buildings with fully unfilled walls, and buildings with an open first floor. The research considered the effects of various factors like infill stiffness, number of bays, SSI, bay width, and the FP of the buildings. The concrete grade, the number of stories, the building’s width and length, and the number of bays are the input parameters used to predict the FP. The FP of RC buildings with and without SSI effects is predicted using the proposed MCAGCNN technique. The proposed MCAGCNN approach improves accuracy by 19.36%, 26.42%, and 23.27%, increases precision by 22.36%, 15.42%, and 18.27%, and reduces RMSE by 18.36%, 16.42%, and 28.27%, compared to the existing techniques, including Genetic Algorithms (GA), Gradient Boosting Decision Trees (GBDT), and Artificial Neural Networks (ANN). The proposed study also demonstrates a lower L∞L∞ norm error of 0.045, indicating a high degree of accuracy and minimal deviation between predicted and actual values.