In this paper, a soft computing approach based on neural networks is presented for the numerical solution of a class of singular boundary value problems (SBVP) arising in physiology. The mathematical model of artificial neural network (ANN) is developed in a way to satisfy the boundary conditions exactly using log-sigmoid activation function in hidden layers. Training of the neural network parameters was performed by gradient descent backpropagation algorithm with sufficient number of independent runs. Two test problems from physical applications have been considered to check the accuracy and efficiency of the method. Proposed results for the solution of SBVP have been compared with the exact analytical solution as well as the solution obtained by the existing numerical methods and shows good agreement with others.