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A video-tactile sensor is being developed to assess the physiological state of the human back muscles. The problem of contact of a linearly elastic spherical head of the sensor with a soft biological tissue is solved. The problem is solved numerically using the finite element method by the ANSYS package. A sample of soft biological tissue was modeled as a round cylinder made of a linearly elastic incompressible material. In addition to the axial force that presses the head against the tissue; additional pressure is applied to the inner surface of the sensor head. Calculation of the stress state of the contact model of the sensor head with the tissue under study makes it possible to estimate the local stiffness of the tissue based on the results of experiments. An estimate of the error in determining the Young's modulus of tissue from a given measurement error of the contact area is given.