With the usage of information technologies in education field, e-assessment that uses information technology to assess students learning started to become popular. Web-based testing, a type of e-assessment, seems to have advantages when compared to traditional testing, like costing, reliability, ease of use etc. Although it seems to have advantages, students' intentions to use web-based assessment tools are needed to be researched to identify the factors that affect students' acceptance of such technologies as well as to enhance these tools by taking into account the needs of users. This paper presents the work in progress in order to determine the factors that affect engineering students' intentions to use web-based assessment systems. The study takes Technology Acceptance Model as a base for research model and by adding new external factors that affect users' intention towards to use web-based assessment which will help the improvement of web-based assessment tools by considering users needs.