The physical properties of arteries are important in the research of the circulatory system dynamics. Moreover, in order to build Virtual Reality Simulators, it is crucial to have a tissue model able to respond in real time. A reduced mesh size results in shorter processing times, which can be achieved using a two-dimensional grid. In this work, a triangular topology is considered and the nodes are connected by three kinds of linear springs (one normal and two angular ones). The spring stiffnesses depend on the mesh geometry and on the elastic properties of the artery. The model linearizes the material response, but it still contemplates the geometric nonlinearities. Comparisons showed a good match with a nonlinear model and with our previous model based on a quadrilateral topology. However, the proposed model extension is more flexible and easier to implement than the previous one.