The primary contribution of this paper is to develop a realistic yet mathematically tractable channel emulator for underwater acoustic communications (UWAC) channels. Our proposed emulator is based on the Wide-Sense Stationary Uncorrelated Scattering (WSSUS) assumption, where the channel samples are generated using finite sum-of-sinusoids (SOS) with uniformly distributed phases. The MATLAB-based Simulink platform and its associated block-set elements are used to generate numerical plots for amplitude distribution, Doppler frequency and channel impulse response. This Simulink-based design offers an added advantage over prevalent UWAC channel simulators, as it can be directly adapted to FPGA platform for hardware implementation.