Simulink is a graphical environment that is widely adapted for the modeling and the Laplace transform based analysis of linear analog circuits used in signal processing architectures. However, due to the involvement of the numerical algorithms of MATLAB in the analysis process, the analysis results cannot be termed as complete and accurate. Higher-order-logic theorem proving is a formal verification method that has been recently proposed to overcome these limitations for the modeling and the Laplace transform based analysis of linear analog circuits. However, the formal modeling of a system is not a straightforward task due to the lack of formal methods background for engineers working in the industry. Moreover, due to the undecidable nature of higher-order logic, the analysis generally requires a significant amount of user guidance in the manual proof process. In order to facilitate industrial engineers to formally analyze the linear analog circuits based on the Laplace transform, we propose a framework, FASiM, which allows automatically conducting the formal analysis of the Simulink models of linear analog circuits using the HOL Light theorem prover. For illustration, we use FASiM to formally analyze Simulink models of some commonly used linear analog filters, such as Sallen-key filters.