An analytical approach to the kinematic analysis of certain types of constant-breadth cam-follower mechanisms has been presented in this paper. The objective of the kinematic analysis is to provide closed-form parametric equations for the displacement, the velocity, and the acceleration of the follower driven by a constant-breadth cam profile rotating at a uniform angular velocity. The follower surface is considered to be a flat-face and the follower motion may either be translatory or oscillatory, or translatory as well as oscillatory. The proposed approach is general in nature and can be used for the kinematic analysis of any profile-closed higher-pair mechanism. Two different cam profiles of constant-breadth, termed as Type I and Type II, have been considered. Numerical examples have been worked out and results of the computational work have been discussed.