Continuous dynamic systems, in juxtaposition to single and/or multiple-degree-of-freedom systems, are those that retain a continuous distribution of the mass, versus lumping the mass at the nodes of a rod and/or a beam element. This results in partial differential equations of motion for the aforementioned structural elements, as compared to the previously obtained ordinary differential equations for the lumped parameter elements, i.e., the SDOF and the MDOF models. Besides the added mathematical complexity, continuous dynamic systems are described by eigenfunctions in a modal analysis environment, as compared to eigenvectors for the lumped parameter systems. The benefit of assuming a continuous mass distribution yields, as expected, higher accuracy in the mathematical modelling of dynamic systems. More specifically, the finite element representation of lumped parameter systems assumes shape functions that are polynomials (up to the fourth degree in terms of the length variable), which are exact representations for the static response of these systems. As such, they yield approximate representations for their dynamic response, and converge to the exact solution as the number of finite elements increases. By way of contrast, the solution for a continuous mass distribution involves trigonometric and hyperbolic functions, which are exact representations of their dynamic behavior. In what follows, we will present the axial (rod) and the flexural (beam) elements, derive their corresponding equations of motion and solve the corresponding eigenvalue problems. Various cases involving the dynamics of continuous systems will be presented, such as moving loads, impact, etc. Finally, a number of numerical examples using the SDE environment will be presented.