A simple and general formalism for the calculation of the "effective mass" necessary for the computation of tunneling corrections by simple one-dimensional models is presented. It is shown that this formalism does not require a priori assumptions regarding the molecularity of the reaction or the relative orientation of the reactive fragments. This method, which we call the Generalized Polyatomic Method, GPM, was used to compute tunneling corrections using the simple Wigner tunneling formalism for the six reactions: H' + H-H --> H'-H + H, CH4 + H --> CH3 + H-2, CH4 + OH --> CH3 + H2O, CH3-CH3 + OH --> CH3-CH2 + H2O and HCN --> CNH. The results obtained in this work indicate that using the "reduced mass" from a direct vibrational analysis of the transition state instead of the "effective mass" could lead to serious errors in the computation of tunneling corrections. This result is very critical given the popularity of this procedure among researchers computing tunneling corrections in gas-phase reactions. Finally, it is also shown that the simple collinear tri-atomic approach (CTM) developed by Johnston is a special case of our more general GPM method. Given its simplicity and computational efficiency, we recommend GPM as the method of choice when computing "effective masses" to be used in one-dimensional tunneling corrections.