Riveted connections are widely used to join basic components, such as beams and panels, for engineering structures. However, accurately modeling joined structures with riveted connections can be a challenging task. In this work, an accurate linear finite element (FE) modeling method is proposed for joined structures with riveted connections to estimate modal parameters in a predictive manner. The proposed FE modeling method consists of two steps. The first step is to develop nonlinear FE models that simulate riveting processes of solid rivets. The second step is to develop a linear FE model of a joined structure with the riveted connections simulated in the first step. The riveted connections are modeled using solid cylinders with dimensions and material properties obtained from the nonlinear FE models in the first step. An experimental investigation was conducted to study accuracy of the proposed linear FE modeling method. A joined structure with six riveted connections was prepared and tested. A linearity check was conducted to validate that the joined structure could be considered to be linear. A linear FE model of the joined structure was constructed using the proposed method. Natural frequencies and corresponding mode shapes of the joined structure were measured and compared with those from the linear FE model. The maximum difference of the natural frequencies was 1.63% for the first 23 out-of-plane elastic modes and modal assurance criterion values for the corresponding mode shapes were all over 95%, which indicates high accuracy of the proposed linear FE modeling method.