Advantages of computer application in design have been repeatedly emphasized. Designers can visualize their abstract ideas rapidly and precisely through various softwares for modeling and drawing. In additions they can generate easily diverse design alternatives within short period of time so that they can devote much more time for creative thinking rather than ordinary time-consuming drawing and model-making jobs. In line with this, a new horizon of computer application in design field has opened in recent years. A wide variety of computer applications, namely expert system for thinking sides of design, has being increasingly introduced. However, there are only few systematic studies on computer application for design education, particularly for two dimensional design. Considering these facts, the main objective of the present study is to develop a systematic procedure for effective computer applications in two dimensional design. This study also aims to develop a computer program which can be used as a design tool in two dimensional design practice. At first, the study reviewed the theory and pratice of computer application and two dimensional design in a basic course, which set the scope of computer applied two dimensional design. Then basic elements for computer modeling and formation (conceptual, visual, and relational elements) have been discussed and analyzed in terms of computer application and two dimensional design. Subsequently, a framework of computer application has been set up for the application on two dimensional design in various ways; concentrating from generation and structure fromulation. Finally, with the findings of study, computer program of Pattern Composition which is far more diversified and much easier than conventional program has been developed and demonstrated to show how computer can be effectively utilized for two dimensional design.