In our institution, we offer a one-quarter long finite element analysis (FEA) class for Mechanical Engineering curriculum. This course teaches computational methods to solve engineering problems using the state of art FEA software ANSYS. The coursework involves teaching fundamental mathematical theories to build the concept, analyzing simple structural problems using matrix algebra, and then solving a wide variety of engineering problems dealing with statics, dynamics, heat transfer and others. Students enrolled in this class solve varieties of problem by analytical approach, finite element approach using matrix algebra, using APDL (ANSYS Parametric Design Language) and ANSYS Workbench. As we are in quarter system, it is challenging to solve additional multidisciplinary complex engineering problems in regular class lectures. Therefore, students enrolled in this class are required to conduct a project solvable by student version of ANSYS within very short time. The project must have adequate engineering complexity conveying interesting knowledge or technical concepts to the entire class. Students have to prepare a brief written report, and share what they have learned with the entire class giving an oral presentation. While a course in FEA could be a common offering in many universities, the author of this paper presents the pedagogical approaches undertaken to successfully implement the course objectives to the undergraduate engineering students. The topics and techniques applied to teach different concepts of FEA to enhance students learning outcomes are addressed in this paper.