Steady blood flow through a circular artery with rigid walls is studied by COSSERAT Continuum Mechanical Approach. To obtain the additional viscosities coefficients, feed forward multi-layer perceptron (MLP) type of artificial neural networks (ANN) and the results obtained in previous empirical works is used. The governing filed equations are derived and solution to the Hagen-Poiseuilli flow of a COSSERAT fluid in the artery is obtained analytically by Homotopy Perturbation Method (HPM) and numerically using finite difference method. Comparison of analytical results with numerical ones showed excellent agreement. . In addition microrotation and the velocity profile along the radius are obtained by using both numerical and analytical approaches.