A prototype computational methodology for reliability assessment of continuum structures using finite element analysis with instability failure modes is described in this paper. Examples were used to illustrate and test the methodology. Geometric and material uncertainties were considered in the finite element model. A computer program was developed to implement this methodology by integrating uncertainty formulations to create a finite element input file, and to conduct the reliability, assessment on a machine level. A commercial finite element package was used as a basis for the strength assessment in the presented procedure. A parametric study for a stiffened panel strength was also carried out. The developed method is expected to have significant impact on the reliability assessment of structural components and systems. This impact can extend beyond structural reliability into the generalized field of engineering mechanics.