Three-dimensional geological model can describe the types of geological information, and express a variety of topological relations among geological phenomena. Kriging interpolation is an important spatial interpolation method of geological modeling, but every grid point needs to compute augmented matrix and solve equations. With the modeling scale and bore data quantity increasing rapidly, we propose to use CUDA which is multi-threaded parallelism to implement parallel Kriging interpolation algorithm. Cutting the geological model can effectively analyze their internal structure, however, the traditional serial cut algorithms are slow when grid quantity is large. We propose a novel geological model poly line cut algorithm using CUDA. The algorithm is based on grid structure, us in poly line to cut stratum surfaces. And then the geological faults can be simulated based on our cut algorithm. We make high speedup and preferable visualization effects finally.