A new numerical technique known as the multi-step transversal linearization (MTL), which is developed within a finite element framework is presented for non-linear transient behavior of isotropic and stiffened plates. In the MTL approach, the non-linear parts of the vector fields are converted to a set of equivalent and conditional forcing terms. These forcing terms are so constructed that the linearized vector field remains identical with the original one at a chosen set of discretization points distributed spatially across the domain of the problem. In the present work, Lagrangian interpolation functions are used to semi-discretize the non-linear part of the operator over the spatial domain. The conditionally linearized vector field thus constructed is transversal to the original vector field at all points of discretization. These operations finally result in a set of non-linear ordinary differential equations for the solution vector, which are solved using Newmark integration technique.