An accurate and efficient numerical model is developed to calculate the earthquake-induced hydrodynamic pressure on uniform vertical cylinders with an arbitrary cross section surrounded by water. According to the boundary conditions and using the variables separation method, the three-dimensional Laplace equation governing the incompressible water is transformed into a two-dimensional (2D) Helmholtz equation. As a key element, a circular boundary surrounding the structures is introduced so that the computational domain is partitioned into unbounded and bounded domains. The unbounded domain is simulated by an exact artificial boundary condition, which is derived by using the separation variable method. The impedance matrix of the entire domain is obtained by the finite-element method. The hydrodynamic forces on rectangular and round-ended cylinders are calculated, which can be modeled as the product of an added mass of water and the acceleration of the cylinder. However, these complicated expressions of the hydrodynamic forces are not suitable for engineering application. Therefore, simplified formulas for the added mass of the round-ended and rectangular cylinders are obtained by the curve-fitting method. The results indicate that the precision of the present added mass formulas is enough for engineering applications.