In the paper, the selected aspects concerning description of viscoelastic behavior of pipe walls during unsteady flow are analyzed. The alternative convolution expression of the viscoelastic term is presented and compared with the corresponding term referring to unsteady friction. Both approaches indicate similarities in the forms of impulse response functions and the parameter properties. The flow memory was introduced into convolution and its impact on the solution was analyzed. To reduce the influence of the numerical errors, implicit Preissmann scheme was applied. The calculation results were verified based on laboratory tests. The study indicated that the flow memory is related to pipe material properties and significantly influences the calculation results. It also showed the role of retardation time in calculations and its relation to flow memory. The proposed approach enabled more detailed analysis of viscoelasticity impact on the pressure characteristics.