The block-up coefficient technique and the finite volume approach are used to solve numerically the complete N-S equations in a square enclosure with spacers. A pressure-velocity correction algorithm (SIMPLE-C, Semi-Implicit Method for Pressure Linked Equation-Consistent) is adopted in the direct calculation of all the physical variables. The applicability, feasibility and efficiency of the block-up coefficient technique applied to simulate three-dimensional viscous flows are investigated.The primary results have shown that the block-up coefficient technique is indeed a simple and convenient numerical approach, with encouraging prospects, for computing the velocity, pressure and other physical quantities for the flows in a channel with complex boundary shape.