In recent times, there has been a rapid increase in technological initiatives to promote electronic commerce. Delivery of services via the Internet or other remote computing technology now represents the trend for most organizations. In keeping with market trends, the banking industry in Jamaica and other countries worldwide have also adapted a variety of technological initiatives to enhance the delivery of services to remote customers. As these trends continue, there is heightened interest in information systems (IS) research to understand the factors that motivate or encourage individuals to use these technologies. This situation exists because interactions in these environments are significantly different from the traditional face to face settings. The original Technology Acceptance Model (TAM) has long been studied, modified, and extended by IS researchers as a classical model for understanding individual's intention to use (IU) an IS. According to TAM, IU an IS is based on two constructs: perceived ease of use (PEOU) and perceived usefulness (PU). Researchers have identified other factors such as trust (TRST) and computer self-efficacy (CSE) that impact an individual's IU an IS. In this predictive study, the researcher examined the integration of TRST and CSE into TAM and their overall impact on customers' intentions to use banking information systems (BIS) in Jamaica. A 32-item Web-based survey instrument was used to collect data from 374 customers of three major banks in Jamaica. A revised TAM model was proposed and SPSS's AMOS 7.0 statistical package was used to perform data analysis and model fit testing based on structural equation modeling (SEM). Results showed that while CSE did not significantly predict TRST and PEOU, it significantly predicted PU. Additionally, TRST significantly predicted both PEOU and PU, and PEOU positively predicted PU and attitude (ATT) towards BIS. Furthermore, PU was a significant predictor of ATT and IU, and ATT significantly impacted IU. The findings also revealed that only TRST varied significantly across males and females and the original TAM had a slightly better fit than the revised TAM. The research laid the foundation for future exploratory studies of TAM in specialized contexts such as BIS in Jamaica.