Triaxial induction tool is an emerging logging tool to detect formation anisotropy including reservoir rocks showing anisotropy such as thin laminated reservoirs. Fast simulation of responses of triaxial tools is very important for efficient inversion and correct interpretation of measurements. We have developed a 1D code (TRITI09) based on the transmission line theory to simulate the responses of triaxial induction tools in multi-layered anisotropic formations. This code can evaluate the nine components of the magnetic fields and apparent conductivity/resistivity for arbitrary oriented triaxial tools. However, the efficiency of the code still needs to be improved. In the code, the most time consuming part is the calculation of the upward and downward reflection wave amplitudes which are dependent on the position of the logging points and the number of modes used in each layer. To improve the efficiency, we are trying to use the same number of modes in each layer in the fast Hankel transform and calculate the upward and downward reflection coefficients only once for a given formation. This project will significantly improve computation efficiency.