This report describes a two dimensioal stochastic process and a program for its simulation. The process can be considered to describe a random track of predetermined length that originates and terminates at predetermined end points. The process is a modification of a process that is without the length and termination constraints. A particular process is defined by the track length, the maximum expected track segment length and the distance between the end points. For motion at a constant speed, the track length constraint is equivalent to a transit time constraint. In Section 2, the process and the unmodified process are described and some of their characteristics are discussed. In Section 3, the simulation program is described. By using the program, graphs and data can be produced that represent realizations of the process. The program, which is written in BASIC, is for an HP-85.