Almost 63% of the goods transported by railways in Brazil use heavy hall trains (long trains with more than 100 vagons over 100 ton). There is a tendency at the Railway Operators to increase the train's length to improve transport produtivity. This strategy increases the loads at the vagon's couplers causing failures. Analytical tools may calculate the dynamic behavior searching ways to minimize the coupler force. This work presents the development of the longitudinal train dynamic simulation model. Mechanical components, physical model and mathematical equations are described. The Transition Matrix obtained from the eigenvectors and eigenvalues and the Convolution Integral are used to solve differential equations of the non homogeneous system. The eigen properties were identified and a braking process was simulated. Modes and natural frequencies are shown and the coupler's maximum longitudinal stress region may be observed in the results.182107116Barbosa, R.S., (1993) Estudo da Dinâmica Longitudinal do Trem, , Dissertaçäo de Mestrado, Universidade Estadual de Campinas (Unicamp), Campinas, São Paulo, BrasilFelicio, L.C., (1984) Modelagem e Simulação do Comportamento Dinâmico de uma Composição Ferroviária, , Instituto de Pesquisas Tecnológicas do Estado de São Paulo S/A IPT, Centro de Desenvolvimento FerroviárioRelatório Técnico no 20.311Garg, V.K., Dukkipati, R.V., (1984) Dynamics of Railway Vehicle Systems, , USA, Academic PressGasch, R., Knothe, K., (1987) Strukturdynamik Diskreter Systeme, 1. , Springer-VerlagMucheroni, M.F., (1994) Introduçäo à Dinâmica dos Sistemas, , Anotações de Aula, Escola de Engenharia de São Carlos EESC - USPSchwarz, R., Identifikation Mechanischer Systeme (1980) Fortschritsberichte der VDI, , Reihe 8 (30)