Cutter suction dredgers are important pieces of rock excavation equipment in port and waterway construction. It is valuable but difficult to properly estimate the cutting force on the chisel pick of the cutter suction dredger. In this paper, an analytical model, called the crushed zone expansion induced tensile failure model (CEIT model), is proposed for rock cutting with a chisel pick in order to predict the peak cutting force (Fc) more accurately. First, a review of the existing models for rock cutting with a chisel pick is presented. Next, based on the tensile breakage theory, cavity expansion theory and some hypotheses, the mathematical formula of the CEIT model is obtained. Different from that in the previous models, the effect of the rock on both sides of the chisel pick on Fc, defined as the sidewall effect is considered in the CEIT model. Then, the predicted Fc by the CEIT model is compared with the predicted Fc by existing theoretical models and experimental results to check the validity of the CEIT model. The results show that the CEIT model can well capture the relationships of Fc to the cutting parameters, including cutting width, cutting depth, and rake angle, and can predict the experimental results much better than the existing models. Finally, the sidewall effect and its influence factors according to the CEIT model are discussed.