We perform some numerical study of the secular triaxial instability of rigidly rotating homogeneous fluid bodies in general relativity . In the Newtonian limit , this instability arises at the bifurcation point between the Maclaurin and Jacobi sequences . It can be driven in astrophysical systems by viscous dissipation . We locate the onset of instability along several constant baryon mass sequences of uniformly rotating axisymmetric bodies for compaction parameter M / R = 0 - 0.275 . We find that general relativity weakens the Jacobi like bar mode instability , but the stabilizing effect is not very strong . According to our analysis the critical value of the ratio of the kinetic energy to the absolute value of the gravitational potential energy ( T / |W| ) _ { crit } for compaction parameter as high as 0.275 is only 30 \% higher than the Newtonian value . The critical value of the eccentricity depends very weakly on the degree of relativity and for M / R = 0.275 is only 2 \% larger than the Newtonian value at the onset for the secular bar mode instability . We compare our numerical results with recent analytical investigations based on the post-Newtonian expansion .