Abstract A fluid inclusion is an idealized form of a defect in a geomaterial. This paper examines the development and decay of pressure within a fluid inclusion, with a spheroidal shape, located in an extended fluid saturated poroelastic medium. In the modelling of the mechanical behaviour of the poroelastic solid, attention is also focused on the possible development of stress-induced damage that can alter the elasticity and permeability characteristics of the porous skeleton. The paper develops a computational approach to the study of the spheroidal fluid inclusion problem and examines the influence of the triaxial stress state, the geometry of the inclusion and damage-induced alterations of the poroelastic response on the celebrated Mandel–Cryer effect for a poroelastic solid. This effect relates to the delayed rise and decay of the fluid pressure in a poroelastic material subjected to three-dimensional stress states.