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We simulate, numerically a waveguide Mach-Zehnder modulator, which is one of the most important components due to its application in high-bit-rate optical communication systems. It can be fabricated in z-cut lithium niobate, where the waveguides are formed by titanium diffusion in LiNbO3 substrate. The device has optimized for high extinction ratio and low insertion loss with symmetric branches and arms using the beam propagation method. The method is used with a rather realistic model of the waveguide structure and applied. to z-cut configuration by including the effects of crystal anisotropy, Ti4+ diffusion, and wavelength dispersion of the refractive index distribution.