The standard step method is commonly used to compute free surface profiles in gradually varied flow (GVF) through open channels. In this study, generalized numerical solutions in the Chebyshev form are presented for the standard step method to compute the free surface profiles in GVF without using look-up tables, interpolation procedures, or simplified assumptions concerning the cross-section geometry. The solutions are obtained using the flow resistance equations of Manning, Chezy, and Colebrook-White. The necessary parameters of some particular cases, namely rectangular, triangular, trapezoidal, circular, and exponential channels, are furnished. The use of the Chebyshev approximation has the advantage of requiring less iteration than the Newton-Raphson approximation. The standard step method is commonly used to compute free surface profiles in gradually varied flow (GVF) through open channels. In this study, generalized numerical solutions in the Chebyshev form are presented for the standard step method to compute the free surface profiles in GVF without using look-up tables, interpolation procedures, or simplified assumptions concerning the cross-section geometry. The solutions are obtained using the flow resistance equations of Manning, Chezy, and Colebrook-White. The necessary parameters of some particular cases, namely rectangular, triangular, trapezoidal, circular, and exponential channels, are furnished. The use of the Chebyshev approximation has the advantage of requiring less iteration than the Newton-Raphson approximation.