In recent years, the topic of existence and exploration of exocomets has been gaining increasing attention. The asymmetrical decrease in the star's brightness due to the passage of a comet-like object in front of the star was successfully predicted. It was subsequently confirmed on the basis of the light curves of stars observed by Kepler and TESS orbital telescopes. Since then, there have been successful attempts to fit the asymmetrical dips observed in the stars' light curves utilizing a simple 1D model of an exponentially decaying optically thin dust tail. In this work, we propose fitting the photometric profiles of some known exocomet transits based on a Monte Carlo approach to build up the distribution of dust particles in a cometary tail. As the exocomet prototypes, we used the physical properties of certain Solar System comets belonging to the different dynamical groups and moving at heliocentric distances of 0.6 au, 1.0 au, 5.0 au, and 5.5 au. We obtained a good agreement between the observed and modeled transit light curves. We also show that the physical characteristics of dust particles, such as the particle size range, the power index of dust size distribution, the particle terminal velocity, and distance to the host star affect the shape of the transit light curve, while the dust productivity of the comet nucleus and the impact parameter influence its depth and duration. The estimated dust production rates of the transiting exocomets are at the level of the most active Solar System comets.