Normal mode coordinates of vibrational states associated with one electronic state are generally different from those of vibrational states associated with other electronic states in polyatomic molecules (normal coordinate mixing). This has prevented the multidimensional Franck-Condon integrals from being widely used in spite of their importance. We introduce a simple, noncumbersome numerical computer method for calculating those integrals despite including a mixing of the normal coordinates in the harmonic oscillator approximation on the basis of the expressions by Sharp and Rosenstock. We also introduce more simple expressions of Sharp-Rosenstock's formulas. (C) 2003 American Institute of Physics.