Vibration exciters are of the most important parts of vibratory technological equipment. Among a great variety of exciters, the inertial ones are currently the most widely used due to their design simplicity, well-studied control techniques, and relatively large efficiency. The present paper deals with a prospective type of inertial exciters based on a planetary mechanism. The main purpose of this research consists in substantiating the possibilities of providing triangular, rectangular, hexagonal, and other paths of oscillations of a single-mass vibratory system driven by a symmetric planetary-type vibration exciter. The mathematical model of the system motion is developed using the Euler-Lagrange equations, and the following numerical modeling is carried out with the help of the Runge-Kutta methods integrated in the Mathematica software. Virtual experiments are conducted in the SolidWorks software using the 3D-model of the vibratory system. The obtained results are presented in the form of time response curves and motion paths of the oscillating body under different operational conditions. The major scientific novelty of the paper consists in substantiating the parameters of the symmetric planetary-type vibration exciter allowing for generating triangular, rectangular, hexagonal oscillations of the single-mass vibratory system. The obtained results can be effectively used while designing new and improving existent vibratory technological equipment, e.g., conveyors, screens, feeders, sieves, etc.