Dissimilar metal welds (DMWs) of the primary loop of French nuclear power plants exhibit complex anisotropic and inhomogeneous material properties. Ultrasonic inspections of such materials are limited due to beam attenuation, skewing and splitting. Accurate numerical simulation tools are useful to optimize Ultrasonic Non Destructive Testing, and develop new signal processing and data reconstruction techniques dedicated to inspection of DMWs. In the past years, several approaches were addressed, either relying on numerical algorithms (finite elements, finite difference-time difference) or semi-analytical techniques (ray-based approaches). This paper presents two ray-based approaches applied to the simulation of DMW inspection. Firstly, the weld material properties are described as a set of anisotropic homogeneous domains. Rays travel in straight lines between two interfaces and reflection coefficients are taken into account as the ray moves from one domain to the next. In the second approach, which is an improved version of the first approach, a smooth description of the grains orientation is considered. Such descriptions may come from a functional form which links the grains orientation to a set of parameters that must be fixed for the considered weld. Alternatively, grains orientation is obtained through an image processing technique applied to metallographic pictures of the weld. Ray propagation is then computed using a dynamic ray tracing algorithm. Here, both approaches are applied to DMWs similar to those found in French nuclear power plants. Simulation results are discussed and compared to finite elements and experimental results.