Current trends of computational tools in the upstream of the petroleum industry are presented herein. Several results and images obtained through commercial programs and through in-house software developments illustrate the topics discussed. They include several types of problems and programming paradigms. Emphasis is made on the future of parallel processing through the use of affordable, open systems, as the Linux system. This kind of technologies will likely make possible new research and industry applications, since quite advanced computational resources will be available to many people working in the area.