This paper presents an approach for finite-time control of a distributed-parameter system : a flexible beam connected to a translational mass. A quasi-tracking variable is introduced, and a terminal sliding mode controller is developed to achieve finite-time convergence of the quasi-tracking variable to a properly pre-defined trajectory. This subsequently provides a set of boundary conditions to explicitly solve the corresponding boundary-value problem and prove finite-time regulation. End-point tracking control is also investigated. It is shown that the error between the end point of the beam and the pre-defined trajectory, though does not decay to zero, is always bounded by a small time-varying bound. A method to reduce the error bound is also given. The approach does not invoke any model truncation procedure, hence the problem of observation/control spillovers, which exists in the conventional truncated-model-based controller design methods, is essentially avoided. Satisfactory simulation results are provided to demonstrate the effectiveness of the presented approach.