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This study presents a strategy of teaching structural line elements involving an open source computer-aided learning tool FreeMat integrated with another open source CALFEM finite element toolbox. One of the important objectives in teaching finite element method at introductory level is to bring students into the comprehension of finite element procedures. Differences are observed in the response of a truck using the rigid bicycle model and the elastic bicycle model. Octave has been used for simulation purpose. These include the steady state solutions as function of different parameters as well as a transient solution in response to a saw-tooth steering input and a step input. Finally, the results of the response study obtained by modelling a small truck with an elastic model and the classical bicycle model are presented. Non-dimensional versions of the equations are used to investigate the steady state response of the model. Complete set of the resulting dynamic equations of this model are presented. This model improves upon the classical bicycle model by taking into account the flexibility of the vehicle frame by using concepts from the Euler beam theory. This paper analyses a modified dynamic model called the "Elastic Bicycle Model". It has widely been used in studying vehicle handling characteristics and designing steering control system for vehicles. The planar rigid bicycle model is one of the most popular models used in vehicle dynamics. The change of rigidity of the frame could give rise to considerable effects in the directional stability and the handling. The elasticity of the frame has an important impact on the directional response (jaw gain, lateral velocity and ultimately the trajectory) of the vehicles. The proposed method offers an easy and quick way to evaluate the dynamic effects in models with flexible frames. MATLAB is used as a platform for evaluation of the dynamics and CALFEM, which is a MATLAB plug-in, is used for the finite element model. The method used is a numerical model of the dynamics coupled with a finite element model of the frame. This work demonstrates that the modified bicycle model is a useful instrument to predict the response of a vehicle. The results obtained show that in the simulations the dynamic effects deteriorate when flexible vehicle frames are considered. In this paper, a method to add elastic effects to the classic ''bicycle model'' for the simulation of the dynamic behaviour of vehicles is presented.