The main objective of this study is testing the hypothesis that the visualization of simulation results creates the conditions for improving students' knowledge, taking into account the specifics of their professional training. In this article we are exploring how the simultaneous use of Excel and GeoGebra can improve the learning outcomes of engineering students in agricultural universities when learning the basics of mathematical modeling (using as example the mathematical model of mechanical movement of two bodies with their elastic collision). We worked with our students as follows. First, we build and interpret the mathematical model. Then we obtain two alternative computer models: we use Excel spreadsheets for numerical modeling as well as GeoGebra software for analytical-geometrical modeling. By this models we visualize and explore the processes closely related to topics that plays an important role in the training of agricultural production engineers, in particular, with study the movement and interaction of particles during the loading / unloading of seeds, the description of industrial processes of seed scarification, with study of the movement of particles of yeast suspension in a plate separators, modeling the processes of shot-blast cleaning of metal surfaces etc. We have tested this approach in teaching the 163 students enrolled in the specialties «Agroengineering» and «Industry Engineering» in Poltava State Agrarian Academy. According to data we collected our students demonstrated a better understanding of the conceptual issues of mathematical modeling and acquired significant abilities in using this method to solve real problems.