: In this thesi we have investigated quantization of Klein-Gordon, Dirac and electromagnetic fields in a finite volume using the method of constrained systems. We consider the given boundary conditions as primary constrains. Consistency of primary constrains leas to infinite chains of constraints. Then, with ought solving the equations of motion, we impose the set of the constraints on a suitably expansion of the fields. We show that if the new set of coordinates, such as Fourier modes , are chosen properly, imposing the constraints omits a few number of canonical pairs. So the reduced phase space, with canonical pairs as coordinates, is achieved. Quantization of the theory then can be done easily by converting canonical coordinates of the reduced phase space to quantum operators. We emphasize that, except consistency of the constraints, the complete dynamics of the system, i. e. solving the equations of motion, is not necessary for quantization.