Abstract: A wavenumber-integration-based method is developed and implemented to provide accurate and stable acoustic field solutions in a Pekeris waveguide. In this method, all the up- and downgoing waves in the homogeneous solution of the depth-dependent wave equation are appropriately normalized, leading to an unconditionally stable system of equations for the amplitudes of the homogeneous solution. For the normal-mode method, in general the contribution from the branch line integral is significant only in the near field. For this reason, the branch line integral is generally ignored in traditional normal-mode models. However, when a mode lies very close to the branch cut, the branch line integral might still contribute to the field significantly at very long ranges. In this case, traditional normal-mode- based models provide inaccurate field solutions because of ignoring the branch line integral. Numerical examples are also provided to compare the present model and a traditional normal-mode model. Numerical results indicate that the present model is accurate and numerically stable, whereas the results by that traditional normal-mode model are inaccurate in certain cases. Hence, the present model can serve as a benchmark model for the problem of sound propagation in a Pekeris waveguide.