Borehole triaxial induction instruments were designed to diagnose and measure rock electrical conductivity parallel and perpendicular to the bedding plane. Experience has shown that the interpretation of triaxial induction measurements often requires numerical modeling for a proper diagnosis of rock electrical conductivity anisotropy in the presence of geometric effects such as dipping wells, layer boundaries, and invasion. We introduce a new algorithm to simulate triaxial induction measurements that combines a Fourier series expansion in a nonorthogonal system of coordinates with a 2D goal-oriented, self-adaptive, high-order finite-element method. This procedure enables the accurate and reliable simulation of triaxial induction measurements across reservoir rock formations with extreme contrasts of electrical conductivity while reducing the 3D computational complexity associated with deviated wells. Numerical results indicate that borehole dip effects on triaxial induction measurements are larger than on standard coaxial induction measurements. The sensitivity of triaxial induction measurements to transversely isotropic rock formations decreases with increasing dip angle.