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In the paper we numerically investigate multiple similarity solutions for the unsteady, incom-pressible laminar flow in a porous expanding or contracting tube.The governing equations are reduced to a singular 4th-order nonlinear boundary value problem by a suitable similarity transformations.We design a combined boundary value (BV)/initial value (Ⅳ) method to obtain all the solutions successfully.We observe that some values of the expansion ratio does not fundamentally change the multiple solutions pattern, and that the combined BV/Ⅳ method is indeed an effective tool for this laminar flow problem, or in particular, for the singular boundary value problem existing multiple solutions.