The pressure induced structural phase transition, elastic and thermal properties of actinide mono-bismuthides AnBi (An=Am, Cm, Cf) have been investigated for the first time by using a modified interionic potential theory (MIPT). This method has been found quite satisfactory in the case of other binary rare-earth actinide compounds. The calculated compression curves, phase transition pressure and bulk moduli for three compounds agree reasonably well with the available experimental results. We have also discussed thermal and elastic properties of these compounds. The calculated values of elastic properties show predominantly ionic in nature.