In this thesis laminar and turbulent channel flows with wall-normal rotation have been investigated by means of numerical and analytical approaches. Contrary to the streamwise and the spanwise rotating channel flow, channel flows with wall-normal rotation has been rarely studied. Since there is no possible experimental approach to the investigation of this flow, they can be studied only numerically and analytically. However, an analytical approach is only possible in the laminar case. In order to establish the effects of the wall-normal rotation on the turbulent channel flow and also to provide reference data for the turbulence case, direct numerical simulations at Re =180, 360 based on the friction velocity in the non-rotating case for various rotation rates (from very small to relatively high) have been performed. It has been found that the both flow states are very sensitive to the wall-normal rotation and are highly affected even with a very small rotation rate. In the turbulent case due to the induction of the spanwise velocity the flow is three-dimensional and as a result all of the Reynolds stress tensor components are non-zero. By increase in the rotation rate relamonarization effects have been observed and finally at very high rotation rates the flow reaches a fully laminar steady state. Further, the Lie symmetry approach has been applied to the Reynolds averaged Navier-Stokes equations describing a turbulent wall-normal rotating channel flow at very high Reynolds numbers to study the ability of this method to predicting the flow. Based on the results, one can conclude that Lie symmetry approach can not deal with the system of differential equations with unclosed terms. Finally the DNS results have been used to investigate the capability of relatively simple turbulence models to predict the flow. In other words we have used the DNS data to validate the simple RANS turbulence models. For weak rotation rates the convincing results indicate that in contrast to the streamwise and the spanwise rotating channel flows, the present flow could be predicted by this simple turbulence model. However, predicting of the flow at higher rotation numbers requires obviously advanced RANS models including relaminarization effects