A parametric study of undrained stability of a spherical cavity in clays is investigated by finite element limit analysis with an axisymmetric condition. Influences of cover depth ratio of cavity and dimensionless overburden factor on predicted failure mechanisms and dimensionless load factor are examined. It is found that a previously recommended and up-to-date lower bound solution to the problem was significantly inaccurate for practice use. Thus, an accurate approximate solution to the problem is proposed from nonlinear regression analysis of the computed average bound solutions. New cavity stability factors for the soil cohesion and soil unit weight are proposed. New findings are revealed for the three-dimensional effect of the cavity shape on these factors between the axisymmetric and plane strain conditions, and their applications to the undrained stability evaluation of cavity problems in practice are described.