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The theoretical derivation of the start‐up laminar flow of incompressible viscous fluid in a long pipe as suggested by Szymanski, could not be verified experimentally. This leads to the checking of assumption of constant pressure gradient across the ends of the pipe, on the basis of which the theoretical development was made. Recently, the problem was again investigated for viscous fluid by Otis. In the present paper, the laminar start‐up flow of elastico‐viscous fluid in a pipe, without assuming constant pressure gradient across its ends, has been investigated. The non‐linear governing equations are solved numerically and the effects of start‐up flow parameters and elastico‐viscous parameter on the velocity distribution have been studied.