A three-dimensional viscoelastic finite element model is developed for cell micromanipulation by magnetocytometry. The model provides a robust tool for analysis of detailed strain/stress fields induced in the cell monolayer produced by forcing one microbead attached atop a single cell or cell monolayer on a basal substrate. Both the membrane/cortex and the cytoskeleton are modeled as Maxwell viscoelastic materials, but the structural effect of the membrane/cortex was found to be negligible on the timescales corresponding to magnetocytometry. Numerical predictions are validated against experiments performed on NIH 3T3 fibroblasts and previous experimental work. The system proved to be linear with respect to cytoskeleton mechanical properties and bead forcing. Stress and strain patterns were highly localized, suggesting that the effects of magnetocytometry are confined to a region extending <10 microm from the bead. Modulation of cell height has little effect on the results, provided the monolayer is >5 micro m thick. NIH 3T3 fibroblasts exhibited a viscoelastic timescale of approximately 1 s and a shear modulus of approximately 1000 Pa.