Queuing networks with Fork/Join mechanisms are encountered in modelling and analysis of parallel computer systems and computer/communication networks. Exact analytical solutions of such networks are not available. In particular, due to the Fork/Join mechanisms, these networks do not have a product-form solution. As a result, approximation methods that can provide accurate estimates of the performance parameters are of high interest. The purpose of this paper is to propose such an approximation method that applies to a fairly general class of closed queuing networks with Fork/Join mechanisms. The method is based on the use of a product-form approximation technique. Numerical results are provided that show that the accuracy of the method is fairly good.