Analytical solutions were obtained for the virtual mass of a Taylor bubble rising in a liquid confined by a circular pipe under transient conditions. The solution of the virtual mass coefficient was based on potential inviscid flow. The present solution is applicable to low viscosity liquids and to Capillary number ($Ca)<0.005$. The virtual mass solution showed dependence on bubble geometry. The present solution was validated by comparison with the available numerical solutions and experimental data of other investigators.