<p>The dynamic analysis of the “truck—central axle trailer” combination, constituting a multibody system, is presented in this paper. The negative phenomenon, known as the “snaking motion”, was considered. A mathematical model of this combination of vehicles was developed by using formalism of Lagrange equations of motion based on the joint coordinates and matrices of homogeneous transformations taken from robotics. The main elements of truck and trailer were modelled as rigid bodies interconnected to form a branched open kinematic chain. The model takes into account the elasticity and damping of the spring-damping elements of the vehicle combination. The generalised forces in the equations of motion resulted from the driving moments, which act on the rear wheels of the truck and the reaction forces of the road surface, which act on the wheels (tires) of the truck and trailer (the Pacejka model of tires was assumed). The introduced constraint equations resulted from assumed courses of steer angles of the front wheels of the truck in the case of simulating different road manoeuvres. The proposed mathematical model was verified indirectly by comparing the results of the numerical analysis with the calculation results obtained using the commercial MSC Adams program. A few design proposals regarding the trailers were formulated based on the results of the performed numerical simulations.</p>