Analytical dynamic modelling of universal multi-mesh geared rotor systems is still quite scarce, even though the theory of single-mesh cylindrical gear pair vibration is extensively studied and well established. Most of these models depend on the basic lumped parameter vectorial formulation to represent the macro behavior of gear mesh kinematics. The method is quite reliable as evident from recent comprehensive literature reviews conducted by Ozguven and Houser [1], and Blankenship and Singh [2]. To address the lack of multi-mesh gear dynamic analytical work, this communication is concerned with the development of a generic n-mesh counter-shaft geared rotor system model. Some of the original attempts to investigate the multi-mesh geared rotor system dynamic problem were by . They analyzed the effects of translational and torsional motions of counter-shafts in dual-mesh systems. However, their analytical formulation is limited to spur gears and only the torsional degrees of freedom (DOF) of the input and output gears are modelled. Lim and Houser [6] also developed a dual-mesh counter-shaft model using a gear representation of 3 orthogonal translational displacements and a single torsional co-ordinate. A more rigorous rigid body gear model with 6 DOF was used by Kahraman [7] to analyze dual-mesh idler gear systems that do not contain a counter-shaft component. The most detailed dual-mesh model yet was established by Vinayak et al. [8,9] to examine geared systems containing a single counter-shaft or idler gear. It incorporates a spatially distributed mesh stiffness formulation proposed by Blankenship and Singh in an earlier paper [10]. Other related studies of single counter-shaft problems include applications of the Ritz-based finite element technique by Velex and Saada [11], and a modal synthesis approach by Choy et al. [12]. Published experimental study involving counter-shaft transmission is even much scarcer. The most elaborate known was conducted by Umezawa et al. [13], which consists of numerous experiments to evaluate the effects of shaft length, input torque, and tooth mesh phase leg on dynamic 0022-460X/99/050905