In the present study is simulated and analyzed the interaction of two dimensional flow past a square cylinder in laminar regime with an upstream mixing layer developed by an axis symmetrical horizontal splitter plate. Mixing layer is generated upstream of the square cylinder by mixing of two uniform streams of fluid with different velocities above and below the splitter plate. A range of upstream domain lengths, the distance between the splitter plate and the square cylinder, and several upstream velocity ratios between the two streams of fluid have been analyzed. Unconfined flow over a square cylinder placed in uniform upstream flow is initially analyzed as it plays a crucial role in understanding properties of the wake. The results are compared with existing literature to validate the code developed and they were found to be in very good agreement. It was observed from the present study that at smaller velocity ratios, the vortices shed into the wake consists of both clockwise and anticlockwise moment vortices. As velocity ratio is increased only clockwise moment vortices were shed downstream and anticlockwise vortices were shed as Kelvin-Helmholtz instabilities.