Engineering education at tertiary level is changing in order to reflect the need for an integrated approach to problem-based learning. Problem-solving techniques related to engineering applications have been used frequently to clarify difficult analytical concepts and theories. However, there is still a need to integrate various engineering disciplines by using different tools and approaches. The main objective of this paper is to present a problem-solving approach to analysis, synthesis and dynamics of mechanisms and machines using computer algebra systems. By using various analytical methods and the graphic capabilities of such mathematical software, it is possible to illustrate and implement, in a creative way, many areas including kinematic and dynamic analysis, vibration analysis and programming. Students generally considered these areas to be difficult.