The present thesis is a theoretical and computational investigation of the effect of J mixing in lanthanide ions on the hyperfine splitting. One of the characteristics of the lanthanide ions is that they retain most of their free-ion character when placed in a solid. In particular J remains a good quantum number. The effect of the crystal-field and magnetic interactions in the solid is to split the manifolds into electronic state with only a small amount of mixing of the manifolds. This small amount of mixing is generally ignored when investigating the magnetic properties of lanthanides in compounds. For the calculation of the hyperfine splitting J-mixing has always been ignored. The present thesis derives a correction factor to be applied to the computed hyperfine splitting parameters to take into account J-mixing. The calculation of the hyperfine parameters in the presence of J-mixing requires the knowledge of the components of the electronic state over the two lowest manifolds. A computer code has been written using Matlab to construct the perturbation Hamiltonian involving two manifolds. The program makes use of published energy gap between the ground and first excited manifold. The crystal field interaction is written in tensor form in order to calculate the off-diagonal elements between different manifolds. Starting from first principle described by Wybourne, the expressions for the dipolar and quadrupolar parameters is recalculated including off -diagonal terms and a simple correction factor is derived. The correction is applied to the computed hyperfine splitting of Ho:LaClz and compared to unpublished NMR measurements. The optical spectrum of Ho:LaCl3 has been extensively studied and accurate crystal-field parameters are available. Our analysis shows that J-mixig reduces the value of the computed dipolar hyperfine splitting by about 3%. This correction actually increases the small discrepancy between computation and measurement. We conclude that our investigation should be extended to the contribution due to intermediate coupling which in the case of holmium mixes some K terms in the ground 'I term; this is expected to increase the computed hyperfine splitting.