With the theories of flexure and bending-stress in beams, established in the eighteenth century by James (Jacob) Bernoulli and Euler (c. 1740) and Coulomb (1773) respectively, Navier developed the analysis of forces and deflexions of beams of varying degrees of complexity, with regard to support and restraint, as part of his extensive and unique researches in theory of elasticity. In those researches, evaluated by Saint-Venant and others (1864), he laid the foundations of modern technical theory of elasticity and anticipated important applications.

It had become well known in carpentry that continuity of beams over supports and building-in the ends of beams, contributed substantially to their strength or carrying capacity. Indeed, Robison had considered this subject in an elementary fashion toward the end of the eighteenth century (Brewster, 1822). Navier was clearly mindful of the common use of such statically-indeterminate construction in timber (to judge by the detail of his illustrations) when he embarked on the precise analysis of systems of that kind and, in the event, his analysis was timely with regard to the development of wrought iron beams and structures, which was stimulated by the needs of railway construction. It was, in fact, the statically-indeterminate beam (including, especially, the continuous beam) which dominated the development of the beam in the nineteenth century.

Navier, 1826

The analysis of encastré and continuous beams is believed to have been published for the first time in Navier's celebrated Leçons of 1826 (though Clapeyron refers to earlier lithographed notes).