2-D computational analyses were conducted for unsteady viscous flow and heat transfer across cylinders of different geometries and different incident angle. Circular, square (both at 0° and 90° angles of incidence) and elliptic cylinders were examined. The calculations were performed by solving the unsteady 2-D Navier-Stokes equations at Re = 100. The calculated results produce drag and lift coefficients, as well as Strouhal number in excellent agreement with published data. Calculations for unsteady, incompressible 2-D flow around a square cylinder at incidence angle of 0° and 45° and for Reynolds number = 100 were carried out. Cycle independence and grid independence results were obtained for the Strouhal number. The results were in excellent agreement with the available experimental and numerical results. Numerical results show that the Strouhal number increases with fluid angle of incidence on the cylinder. The wake behind the cylinder is wider and more violent for a square cylinder at 45° incidence compared to a square at 0° this is due to the increase in the characteristic length in the flow direction. The present studywas carried out for a 2-D single cylinder at fixed location inside a channel for unidirectional velocity. To get more accurate results computation on 3-D geometry should be carried out.