In the present article, we have investigated the high-pressure structural phase transition of lanthanide and actinide bismuthides (LaBi, CeBi, PrBi, CmBi, PuBi and UBi). A modified interaction potential model (MIPM) (including the covalency effect) has been developed. Phase-transition pressures are associated with a sudden collapse in volume. At compressed volumes, these compounds are found either in tetragonal or CsCl phase. The phase-transition pressures and associated volume collapses obtained from present potential model show a generally good agreement with available experimental data from others. The elastic constants and their pressure derivatives are also reported. Moreover, the thermodynamical properties have also been obtained successfully. Our results are in general in good agreement with experimental and theoretical data where available, and provide predictions where they are unavailable.