This project work is concerned about some simple analytical solutions of laminar and incompressible viscous fluid flows. Particularly it deals about the velocity distributions of some simple fluid flow problems (Couette and Poisueille) flows. Solving non-linear Navier- Stokes equations are complex and difficult. To reduce this complexity and difficulty we have considered one-dimensional, laminar and incompressible viscous fluid flow problems. we have been used mat lab codes to solve those fluid flow problems analytically.