In this paper, we invoke system theoretic principles and matrix calculus to build higher-order sensitivity models. The approach clarifies and generalizes many of the procedures used in finite element models at present. There are three key features of the work: higher-order sensitivity models in a transformed space of basic variables are found routinely, row and column sensitivities are found without the superfluous notion of the adjoint system, and, the approach is computer worthy. The work has applications in linear and nonlinear networks, structures and finite element models, and FORM and SORM structural reliability. A detailed analysis of a simple truss problem is presented.