The ultimate mechanical properties of MgSiO3 orthoenstatite (OEN), as characterized here by the ideal strengths, have been calculated under tensile and shear loadings using first-principles calculations. Both ideal tensile strength (ITS) and shear strength (ISS) are computed by applying homogeneous strain increments along high-symmetry directions ([100], [010], and [001]) and low index shear planes ((100), (010), and (001)) of the orthorhombic lattice. We show that the ultimate mechanical properties of OEN are highly anisotropic during tensile loading, with ITS ranging from 4.5 GPa along [001] to 8.7 GPa along [100], and quite isotropic during the shear loading with ISS ranging from 7.4 to 8.9 GPa. During tensile test along [100] and [001], a modified structure close to OEN has been found. This modified structure is more stable than OEN under stress (or strain). We have characterized its elastic and ultimate properties under tensile loading. With ITS ranging from 7.6 GPa along [010] to 25.6 GPa along [001], this modified structure appears to be very anisotropic with exceptional strength along [001].