We use the time‐dependent Navier–Stokes equation to study the dynamics of a liquid rising in a capillary tube. We show that the evolution consists of an initial stage of inertial motion, followed by a dynamical‐balance stage in which gravity and viscosity compensate the capillarity force. This approach is compared with other formulations, based on the study of variable mass systems or on some simplified hydrodynamical formulas. Our attention is then focused on the crossover between the regimes of monotonic and oscillatory motion, and we find that numerical solutions to the relevant equations are in good agreement with an analytical linearized approach.