Magmatic unrest can be successfully monitored and studied from modeling of the induced surface deformation; one limiting factor however is the small number of available magmatic source models. Here we have obtained expressions (quadrupole approximation) for displacements and stresses from the inflation of any pressurized triaxial ellipsoid in an infinite elastic medium. The expressions can be evaluated by combining the effects of seven suitable point sources and are approximately valid also for a heterogeneous half-space. Till now, the only available (approximate or exact) expressions for finite expansion sources referred to spheres, prolate spheroids, and horizontal circular cracks embedded in a homogeneous half-space. Our approach allows to model also oblate spheroids and non-axisymmetric sources, whose effects were previously estimable only in the far field through a moment tensor representation. We also show that when the deformation source is a vertically flattened ellipsoid, the inversion of superficial displacements using a general moment tensor may lead to wrong physical models of the deformation source itself. This may be the case for the Campi Flegrei caldera, as well as for other calderas.