Efficient numerical procedures (modal method) for solving large-scale, sparse, nonlinear large-deflection random vibration problems are reviewed. Solution for the small number (say less than 100) of lowest linear eigen-pairs needs to be solved for only once, in order to transform nonlinear large displacements from the conventional "structural" degree-of-freedom (dof) into the "modal" dof. The reduced coupled nonlinear equations of motion in modal dof can be inexpensively solved by the popular Runge-Kurta (RK) or any other time integrating method. The main focus of this work will be placed upon computational issues involved in the nonlinear modal methodologies. Major time consuming portions of the nonlinear modal method are firstly identified. Then, efficient sparse and dense matrix technologies are proposed and incorporated into the developed procedures. Small, medium, and large-scale single panel models are used to validate and evaluate their numerical performance. Comparisons (in terms of numerical accuracy and computational time) between the developed code with existing solution, including popular commercialized finite element software, such as ABAQUS are included, whenever possible. Results obtained to this date indicate that the developed algorithms and software are accurate and highly efficient.