There has been considerable interest in the development of parallel algorithms, even before parallel computers became available. Commercially available parallel computers have provided further impetus to the research on the design of efficient parallel algorithms for solving various problems. There are a variety of ways that parallel processing can be classified. It can be considered from the internal organization of the processors, from the interconnection structure between processors, or from the flow of information through the system. One classification introduced by M. J. Flynn considers the organization of a computer system by the number of instructions and data items that are manipulated simultaneously. This thesis is about the study of some fast and efficient algorithms for Single-Instruction Multiple-Data (SIMD) computer and the analysis of their complexities, and also to design a simulation system for implementing these parallel algorithms using the Modula-2 language. There are three main reasons for using such a Modula-2 language, these are: It is exceptionally consistent. That is, there are no "little things" to remember that have to be performed to do things; it is uncluttered with needless features. It provides an excellent support environment for large, multiple-programmer projects, and It provides excellent support for concurrent programming, which is important to build the simulation system of the parallel algorithms. The proposed system was implemented on a 80486DX-2 100 MHz computer, with DOS ver 6.0 or higher, 4 MB RAM, using TopSpeed Modula-2 language Version 1.16.