Simulations of oscillatory motion in partially filled rectangular tanks with different tank geometries, fullness ratios, and motion frequencies are presented. Smoothed particle hydrodynamics (SPH) method is used to discretize the governing equations together with new velocity variance-based free surface (VFS) and artificial particle displacement (APD) algorithms to enhance the robustness and the accuracy of the numerical scheme. Two-dimensional (2D) oscillatory motion is investigated for three different scenarios where the first one scrutinizes the kinematic characteristics in resonance conditions, the second one covers a wave response analysis in a wide range of enforced motion frequencies, and the last one examines the dynamic properties of the fluid motion in detail. The simulations are carried on for at least 50 periods in the wave response analysis. It is shown that numerical results of the proposed SPH scheme are in match with experimental and numerical findings of the literature.