We define dislocation Love numbers <hijnm,lijnm,kij nm,lt,ijnm> and Green's functions to describe the elastic deformation of the Earth caused by a point dislocation and study the coseismic displacements caused in a radially heterogeneous spherical Earth model. We derive spherical harmonic expressions for the shear and tensile dislocations, which can be expressed by four independent solutions: a vertical strike slip, a vertical dip slip, a tensile opening in a horizontal plane, and a tensile opening in a vertical plane. We carry out calculations with a radially heterogeneous Earth model (1066A). The results indicate that the dominating deformations appear in the near field and attenuate rapidly as the epicentral distance increases. The shallower the point source, the larger the displacements. Both the Earth's curvature and vertical layering have considerable effects on the deformation fields. Especially the vertical layering can cause a 10% difference at the epicentral distance of 0.1¿. As an illustration, we calculate the theoretical displacements caused by the 1964 Alaska earthquake (mW=9.2) and compare the results with the observed vertical displacements at 10 stations. The results of the near field show that the vertical displacement can reach some meters. The far-field displacements are also significant. For example, the horizontal displacements (u&psgr;) can be as large as 1 cm at the epicentral distance of 30¿, 0.5 cm at about 40¿, magnitudes detectable by modern instrument, such as satellite laser ranging (SLR), very long baseline interferometry (VLBI) or Global Positioning System (GPS). Globally, the displacement (ur) caused by the earthquake is larger than 0.25 mm. ¿ American Geophysical Union 1996