Acoustic particle velocities can provide additional energy flow information of the sound field; thus, the vector acoustic model is attracting increasing attention. In the current study, a vector wavenumber integration (VWI) model was established to provide benchmark solutions of ocean acoustic propagation. The depth-separated wave equation was solved using finite difference (FD) methods with second- and fourth-order accuracy, and the sound source singularity in this equation was treated using the matched interface and boundary method. Moreover, the particle velocity was calculated using the wavenumber integration method, consistent with the calculation of the sound pressure. Furthermore, the VWI model was verified using acoustic test cases of the free acoustic field, the ideal fluid waveguide, the Bucker waveguide, and the Munk waveguide by comparing the solutions of the VWI model, the analytical formula, and the image method. In the free acoustic field case, the errors of the second- and fourth-order FD schemes for solving the depth-separated equation were calculated, and the actual orders of accuracy of the FD schemes were tested. Moreover, the time-averaged sound intensity (TASI) was calculated using the pressure and particle velocity, and the TASI streamlines were traced to visualize the time-independent energy flow in the acoustic field and better understand the distribution of the acoustic transmission loss.