<p>This works presents the free vibration and nonlinear analysis of a flexible L-shaped beam with rigid tip mass undergoing coupled in-plane, out-of-plane and torsional deflections. A general eccentric tip mass having inertia is considered at the proximal end of second beam and beams are modelled as Euler-Bernoulli beam element. The dynamic modelling is accomplished by expressing the position and velocities of the multi-body system in terms of inertial and multi-floating co-ordinates. and subsequently applying the Hamilton’s principle. The geometric and inertial nonlinearities in the system are retained in governing equations by considering inextensibility condition. The theoretical linear modal analysis of the system with a geometrically asymmetric tip mass is performed by solving six sets of linearly coupled partial differential equations and twenty boundary conditions. Further, the dynamic response of the system undergoing flexural-torsional vibrations is accomplished by using method of multiple scales. The steady state solutions incorporating inherent 1:1:1:1 internal resonance in presence of external excitations are obtained. In case of modal parameters, numerical solutions are compared with those in existing literature and a close agreement is found with FEA simulations. The reported outcomes have been substantiated by comparing analytical and numerical results. The comparative eigenfrequencies and frequency responses are presented for the variations of critical system parameters. The present work shall serve as an important step in developing and analyzing the refined nonlinear models of L-shaped beam structures used in various mechanical and civil applications.</p>