Water is the most important chemical component on Earth. Seawater distillation processes have a considerable promise as a technique suitable for producing large scale quantities of potable water from the seawater. Distillation process flowsheets consist of a number of interconnected units. The development of the mathematical model describing the behaviour of these units, and the subsequent solution of this model are fundamental steps in process flowsheeting. The first objective of this work is to develop a specialized flowsheeting program for performing design and simulation calculations for different types and configurations of seawater distillation processes. Many numerical methods have been used for solving linear and nonlinear sets of equations representing distillation processes. Most of these methods involve the direct manipulation of the mathematical model equations without exploiting the special properties, such as the sparsity and the weak nonlinearities, of these equations. The second aim of this study is to develop a new approach taking advantages of these properties. Hence, the model equations can be linearized, and grouped according to the variable type. These groups can then be solved by linear matrix technique. The performance of the developed program is investigated by solving many distillation process problems. The results from design and simulation calculations for large practical desalination plants are discussed. In addition to that the convergence characteristics of the new approach (such as stability. number of iterations. computing time. sensitivity to starting values, and general ease of use) are presented. Also. the validity of the approximation assumptions proposed to develop the new approach is examined.