The electronic structures, densities of states, Fermi surfaces and elastic properties of AB3 (A =La, Y; B =Pb, In, Tl) compounds are studied under pressure using the full-potential linear augmented plane wave (FP-LAPW) method within the local density approximation for the exchange-correlation functional and including spin-orbit coupling. Fermi surface topology changes are found for all the isostructural AB3 compounds under compression (at V/V0 = 0.90 for LaPb3 (pressure = 8 GPa), at V/V 0 = 0.98 for AIn3 (pressure = 1.5 GPa), at V/V0 = 0.80 for ATl3 (pressure in excess of 18 GPa)) apart from YPb 3, although its electronic structure at zero pressure is very similar to that of LaPb3. For LaPb3 a softening of the C 44 elastic constant under pressure (equivalent to 8 GPa) may be related to the appearance of a new hole pocket around the X point. From the calculated elastic properties and other mechanical properties, all the compounds investigated are found to be ductile in nature with elastic anisotropy. The states at the Fermi level (EF) are dominated by B p states with significant contributions from the A d states. For the La compounds, small hybridizations of the La f states also occur around EF. © 2013 IOP Publishing Ltd.