In the literature, the relationships between the modes of operation of the buried-channel MOSFET and the potential and signal electron distribution within the device is unclear. In this paper we present a new analytic model for the potential and electron distribution in the channel-depth direction for the buried-channel MOSFET. The purpose of our model is to aid in the fundamental physical understanding of the operational modes of the BC-MOSFET and the mechanisms affecting these modes. Using Poisson's equation individual analytic expressions are formulated to predict the potential distribution and electron concentration profile under conditions of depletion, inversion, pinchoff, and accumulation as a function of the gate bias, substrate bias, and the applied channel potential. The model is general and is used here to represent the potential distributions for both the normally-on and normally-off type BC-MOSFET under various bias conditions. While the potential distribution in the channel depth direction enables one to visualize the band-bending within the device, the signal electron concentration profile leads to an easy physical interpretation of the modes of operation and the location of mobile charge relative to the channel surface: this is important for mobility and device speed considerations. In addition, our developed model can be used for device design. It predicts the effects of doping density concentration both in the substrate and in the channel region, channel implant depth, and oxide thickness on the operating regimes of the device.