Supercavitating vehicles have received significant attention in military applications due to their high underwater speed. This paper aims to establish an analytical model of the encounter probability between a supercavitating vehicle and its target in two modes: straight-running mode (SRM) and turningstraight-running mode (TSRM), providing the basis for combat decision-making. We propose a mathematical model for the supercavitating vehicle to encounter the target in SRS and TSRS. An improved particle swarm optimization (PSO) algorithm based on local best topology with a penalty function is introduced to plan the TSRM path of the supercavitating vehicle. The particle swarm position is updated by using Cauchy and Gaussian distributions. The Monte Carlo simulation method considering the target scale is employed to determine the judgement indexes of the encounter probability analytical models in SRS and TSRS through statistical analysis. Based on the law of error propagation, the analytical models of judgement index variances in the two modes are derived by using the implicit function differential method, and the integral interval of the analytical models of encounter probability is obtained according to the relative motion of the supercavitating vehicle and target. Monte Carlo simulation and hypothesis testing are utilized to verify the accuracy and feasibility of the encounter probability analytical models between the supercavitating vehicle and the target.INDEX TERMS Supercavitating vehicle, encounter probability, path planning, Monte Carlo method, the law of error propagation.