In the near future, to study the surface layer of various cosmic bodies (planets, asteroids, comets), the use of high-velocity penetrators capable of penetrating into it due to their existing reserve of kinetic energy is being considered. Research penetrators are equipped with sensors and devices for various purposes, the maintaining functionality of which depends on the penetrator overload during penetration. The penetration depth of penetrators and the overload that they experience are determined by the resistance force of the soil-rock target acting on the penetrator, considered as a non-deformable solid body. Actual problems for research penetrators are to increase the depth of their penetration into soil-rock targets and reduce the overloads that they experience. Based on the local interaction theory, a comparative analysis of the resistance of soil-rock targets to the penetration of penetrators with a conical and “power-law” head shape was carried out. The generatrix of the “power-law” head is described by a power-law equation. The influence on the penetration parameters of the relative height of the “power-law” head and the exponent in the equation of its generatrix was determined. It has been established that at certain values of the exponent, penetrators with a “power-law” head can have a slight advantage in the depth of penetration into soil-rock targets and the experienced overload in comparison with penetrators with a conical head at the same height of the heads. The choice of the optimal exponent value in the head generatrix equation depends on the specific penetration conditions (penetrator velocity and type of soil-rock target).