The law of conservation of energy and the law of conservation of momentum are two fundamental laws of physics. This study investigates student comprehension of these concepts at the first year of the two technical faculties of the University of Zagreb, the Faculty of Electrical Engineering and Computing and the Faculty of Civil Engineering. The research was conducted on 45 students. The problems used in the study are at high school level and they examine the understanding and application of the energy conservation law and the law of conservation of momentum, the concept of transformation of various forms of mechanical energy and the concept of work. Problems of different difficulties were used, from simple ones that require application of only one physical law, to more complex ones that require the use of more physical principles and more steps in solving. The impact of the figures that the students drew on problem solving was also analyzed. The students have poorly solved the test indicating to the difficulties in understanding and application of the concepts mentioned above, while a detailed analysis of the solutions and figures that the students have drawn has indicated to the problems in comprehension and visualization of various physical situations.