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Cytomagnetometry is a noninvasive method to investigate intracellular movements of organelles such as phagosomes by introducing magnetic particles into cells by phagocytosis, magnetizing them and measuring the field from the cells. To analyze the results of the cell-field measurement, the authors introduce a model for intracellular phagosome motion and investigate their behavior in terms of the cell field. The model includes an elastic body and two viscosity components which are ascribed to the filamentous structures surrounding the phagosomes. The magnetic relaxation phenomenon is assumed to derive from the rotationary Brownian motion as in the authors' previous model. Although the model is simple, its behavior is not trivial because it contains a nonlinear term and the Brownian motion term. This model is the simplest one possible having a viscoelastic body and its behavior hence should be investigated thoroughly.