We develop and extend theoretical and computational methods for the calculation of the deformation, gravity and potential change due to a point source of magma injection into a multilayered, elastic-gravitational earth model. In our calculations, which are based upon the method outlined by Rundle, two distinct layers overlying a half-space may be incorporated. The source can be located in either of the layers or the half-space. The method is quite general, and can be readily adapted to calculations in which stresses in either the layers or the half-space relax by viscoelastic flow. The results obtained indicate that the use of homogeneous half-space to represent the Earth may in some cases be too simple a model and that variations in elastic moduli have a more significant effect than variation in reference density on both the surface displacements and gravity changes. As an example, we calculate the displacement and gravity changes due to a subsurface mass injection in a crust-mantle model appropriate to the volcanic island of Lanzarote, which is presently the subject of numerous geophysical experiments. Both historical and recent data indicate that Lanzarote may be subject to some risk of volcanic eruption in the future, thus our calculations may be useful in interpreting observations of preeruption phenomena. The results are discussed in terms of prediction versus measurement capabilities.