In this work., three typical model potential functions were used to calculate the matrix shifts in THE GROUND VIBRATIONAL - ROTATIONAL V-R LEVELS OF H2, D2 AND HD, IN KR, KR AND X ATRICESTHEPARAMETERS OFThese potential functions (the Lennard- Jone potential, the one parameter, and the three . parameter Buckingham-Corner potential) were calculated using different methods, and were compared to the available experimental data and other theoretical calculations. The effect of anisotropy was added, and showed to cause a fine splitting between the shifts in the transitions of the purely rotational and vibrational-rotational levels. The average of the Legender polynomial was calculated with the aid of the Racah coefficients. The effect of the distortion on the lattice parameter (a) was added, and a theoretical model was constructed to ucacribe this effect. The model was built on the assumption .that the host to be considered neutra. spherts, and included all the parameters believed to cause distortion. The matrix shift results were compared to the available experimental data, and other theoretical models, and showed to be highly accurate, especially for H2 -Ar.