Robot artistic painting and robot calligraphy do require brush models for brushstroke simulation and painting robot control. One of the main features of the brush is its compliance, which describes the relationship between the brush footprint shape and the pressure applied to the brush. In addition, during motion, the brush footprint position lags from the brush handle position in a complicated manner. To date, the question of creating a physically correct model of these effects and choosing the best method for the model parameter calibration has not been presented in the literature. In the current paper, we derive equations of the brush contact patch motion, give their closed-form solutions, and investigate three methods for the brush model calibration: capturing brush footprints on a matte glass with a camera, painting calibration brushstrokes, and capturing a brush shape side projection with a camera. As we show, calibration brushstrokes give us primary information on brush contact patch displacement during painting, and capturing the brush side projection allows the accurate estimation of the gap from the brush tip to the center of the contact patch. Capturing brush footprints is useful for creating a brushstroke executable model. As an example, a model for a round artistic brush was created and verified in three tests, including measuring the coordinates of an angular brushstroke center line, simulating an angular brushstroke, and writing a signature using a robotic setup.