The analysis of previous works devoted to experimental studies of the frequency characteristics of the body of a sitting human body subjected to vibration and the construction of its mechanical models is conducted. It is noted that in most cases measurements of vibration are made on the seat and the head of the person that allows us to build a transmission function from the seat to the head. In doing so, the supposed internal structure of the human mechanical model remained unconfirmed. Under these conditions, it was emphasized that vibration measurements should be performed on all modeled parts of a human body. In addition, from an anatomical point of view, the main contribution to the mechanical properties of the body of a sitting person is made by the multi-jointed muscles of the spine. However, this important fact has not been taken into account yet. In this regard, the task was set to study the influence of multi-articular muscles on the frequency properties of the body of a sitting person. For this purpose, a number of mechanical models were constructed in which multi-jointed muscles were modeled by multi-link viscoelastic connections. In particular, on the simplest model with two degrees of freedom it was shown how the imposition of two-link connections in addition to a single-link one leads to the appearance of an anti-resonant frequency on the upper mass, that is impossible in their absence. A mechanical model with an arbitrary number of degrees of freedom with multi-link connections is given, for which the formulas of the transfer function and the amplitude-frequency response for the upper mass are obtained. In addition, we consider a mechanical model with an arbitrary set of multi-link connections. As an example, the results of numerical calculation of the frequency response for a mechanical model with eight degrees of freedom in the presence and absence of multi-link connections are given.