Ab initio total-energy calculations and X-ray diffraction measurements have been combined to study the phase stability of zirconate pyrochlores (A(2)Zr(2)O(7); A = La, Nd and Sm) under pressures up to 50 GPa. Phase transformations to the defect-cotunnite structure are theoretically predicted at pressures of 22, 20 and 18 GPa, in excellent agreement with the experimentally determined values of 21, 22 and 18 GPa for La(2)Zr(2)O(7), Nd(2)Zr(2)O(7) and Sm(2)Zr(2)O(7), respectively. Analysis of the elastic properties indicates that elastic anisotropy may be one of the driving forces for the pressure-induced cubic-to-noncubic phase transformation.