A dynamic stability analysis model is developed for meniscus-defined crystal growth processes. The Young-Laplace equation is used to analyze the response of a growing crystal to perturbations to its radius and a thermal transport model is used to analyze the effect of perturbations on the evolution of the crystal-melt interface. A linearized differential equation is used to analyze radius perturbations but a linear integro-differential equation is required for the height perturbations. The stability model is applied to detached solidification under zero-gravity and terrestrial conditions. A numerical analysis is supplemented with an approximate analytical analysis, valid in the limit of small Bond numbers. For terrestrial conditions, a singularity is found to exist in the capillary stability coefficients where, at a critical value of the pressure differential across the meniscus, there is a transition from stability to instability. For the zero-gravity condition, exact formulas for the capillary stability coefficients are derived. Published by Elsevier B.V.