We develop a method for taking target mass effects into account for the structure functions of inelastic lepton-hadron scattering using analytic moments in the variable s instead of the well-known Nachtmann variable £ and Bjorken variable x. We find new expressions for the structure func­tions F1, F2, and F3 that depend on the target mass and agree with the spectral property. We demonstrate that these new expressions, which take mass corrections into account for the structure functions, lead to results that differ significantly from the results obtained both using the standard £ method and using the method suggested by Steffens-Melnitchouk, es­pecially for values Q2 of the order of several GeV2 and for large values of x.