In this work, a computational fluid dynamics (CFD) model is developed to simulate the dynamics of meniscus formation and capillary flow between vertical parallel plates. The arbitrary Lagrangian-Eulerian (ALE) method is employed to predict and reconstruct the exact profile of the meniscus with no need for implicit interface tracking schemes. The capillary pressure differential resulting from the curvature of the liquid-gas interface is applied as a boundary condition at the liquid-gas interface. The model is used to simulate the rise of water flow and the evolution of the meniscus between two parallel aluminum plates with various wall spacings ranging from 0.5 mm to 3 mm. The liquid-solid contact angle is fixed at θ = 73°. The equilibrium height predicted by the CFD model showed a very good agreement with that obtained from the Young-Laplace equation, with an error of less than 1%. Furthermore, the model was verified by comparing the steady-state meniscus profile with analytical solutions, and excellent agreement was observed. In the absence of accurate analytical models for predicting the dynamic behavior of capillary flow between parallel plates, the developed model presents a novel approach for simulations of the transient response of such capillary flows.