Mass, wing length, tarsus length and four bill dimensions were measured on adult Large Cactus Ground Finches (Geospiza conirostris) and their offspring in a field study on Isla Genovesa, Galapagos. Heritabilities of these traits were determined by regressing family mean offspring values on midparent values. Principal components analysis was used to provide a multivariate characterization of size and shape, and component scores were used in heritability analysis. Morphological traits were highly heritable. All heritabilities of univariate traits exceeded 0.65, and the arithmetic mean was 0.84. Principal component 1 provides a measure of overall body size; this has a high heritability (0.79). Principal component 2, a bill-pointedness shape factor, also has a high heritability (0.92). Indirect evidence suggests the possibility of a small influence of genotype--environment correlation on the heritability estimates for two traits, mass and bill length. The overall conclusion is that there is a strong potential for evolutionary change in morphology in this population. The population may have been subject to disruptive selection recently, followed by stabilizing selection. Genetic correlations between measured traits were moderately large (mean 0.54) and all were positive. In several respects G. conirostris is intermediate between two other congeneric species, G. fortis and G. scandens. Heritabilities and genetic correlations appear to be higher in G. fortis and lower in G. scandens. These differences are associated with different feeding niches, different degrees of predictability of food resources and different types of selection pressures to which the species are subjected.