Over the years, various reports confirmed the importance of complex problem-solving in the workplace. However, in most cases, engineering educators often fail to design assessment rubrics that drive the ability to solve complex problems among the students. Literature review revealed that the studies of assessment rubrics in higher education have been undertaken in a wide range of disciplines but not in the field of engineering. Hence this study attempts to present the gaps in four assessment rubrics which were designed to assess engineering design projects. It applied comparative case studies to analyze and synthesize the similarities, differences and patterns from the assessment rubrics to produce generalizable knowledge about how and why particular assessment rubrics work or fail to work against the attributes of complex engineering problem solving and complex engineering activities defined by the International Engineering Alliance (2013), and the essential features of rubrics proposed by James Popham (1997). The results showed that engineering rubric designers generally fulfilled the requirements of designing a rubric. The shortcomings, however, it was found that not all-important design skills were addressed and limited characteristics of complex engineering problem solving were practiced by engineering educators, and the absence of complex engineering activities in the design of assessment rubrics. The understanding of these shortcomings is expected to benefit engineering educators in enhancing their instructional materials for implementing complex problem solving in engineering design projects and subsequently improve the ability of the engineering graduates to solve complex problems.