Multi-span fluid-conveying pipelines (MFP) with multiple concentrated accessories, i.e., clamps, valves, flanges, vibration absorbers and flexible components, whose dynamic properties can be described by receptance, are widely used in many engineering fields. However, research on predicting the dynamics of such pipe structures has been rarely performed. In this study, we propose an improved transfer matrix method (TMM) to model the numerically stable dynamics of the MFP with multiple concentrated accessories and flexible components. An original receptance-based modeling method is developed to address boundary conditions induced by the presence of concentrated accessories and flexible components simultaneously. The method's advantage is that the flexible component is considered as an independent substructure before assembling, its receptance can be calculated or measured independently. Moreover, the numerical instability problem of the conventional transfer matrix method (CTMM) in the high-frequency range is resolved by utilizing a successive reduction process to reduce the length of the transfer path of the state vectors used to describe the overall dynamics of the pipe. One salient feature of the proposed method is that the size of the characteristic matrix will be specified as 4×4, which is inherited from CTMM. An optimization-based inverse method is proposed to identify the clamp stiffness with the developed numerically stable and efficient dynamics model. Also, a device is designed and developed to measure the approximate clamp stiffness values which are considered as the initial values during optimization. The experimental results indicate that the proposed method is effective and accurate; utilizing the approximate values of the clamp stiffness as the initial values can accelerate the stability of the iteration during the optimization.