On the basis of generalized Sturm theory, this paper presents a simple, but systematic approach to the delay-independent stability analysis of the linear dynamic systems involving multiple degrees of freedom and possibly two time delays. The approach enables one to complete the stability analysis in a much simpler way than before through the use of a MAPLE routine given in the paper. To demonstrate the approach, the paper gives a detailed analysis, the corresponding sufficient and necessary conditions as well as stable regions in parameter space of concern for the delay-independent stability of a vibrating system with time delays in state feedback, an active-tendon for a tall structure and an active suspension of a quarter car model.