Here, a simplified analytical model has been proposed to predict solid fraction, solid-liquid interface, solidification time, and temperature distribution during solidification of phase change material (PCM) in a two-dimensional latent heat thermal energy storage system (LHTES) with horizontal internal plate fins. Host of boundary conditions such as imposed constant heat flux, end-wall temperature, and convective air environment on the vertical walls are considered for the analysis. Heat balance integral method was used to obtain the solution. Present model yields closed-form solution for temperature variation and solid fraction as a function of various modeling parameters. Also, solidification time of PCM, which is useful in optimum design of PCM-based thermal energy storages, has been evaluated during the analysis. The solidification time was found to be reduced by 93% by reducing the aspect ratio from 8 to 0.125 for constant heat flux boundary condition. While, for constant wall temperature boundary condition, the solidification time reduces by 99% by changing the aspect ratio from 5 to 0.05. In case of convective air boundary surrounding, the solidification time is found to reduce by 88% by reducing the aspect ratio from 8 to 0.125. Based on the analytical solution, correlations have been proposed to predict solidification time in terms of aspect ratio and end-wall boundary condition.