The modeling of compliant bridge-type displacement amplification mechanisms has challenges due to the intrinsic coupling of kinematic and mechanical behaviors. A structure load performance integrated model method for the bridge-type displacement amplification mechanism is presented. The established modeling based on Castigliano's second theorem considers the deformations of all members, the effect of external load and the nonlinear shear effect. Compared to the finite element model (FEM) and existing models, the established modeling precisely predicts significant nonlinearity of the displacement amplification ratio (DAR) with the driving force, strong sensitivity of DAR to the external load and corresponding relationships of structural parameters with DAR, which is the closest to the FEM result over existing models. The variance-based sensitivities of structural parameters to DAR are thoroughly analyzed, indicating that sensitive structure parameters need to be focused on. Modeling applications further prove the reliability and expandability of the proposed model method. The proposed model method can provide support for the design, optimization and control of compliant systems with bridge-type displacement amplification mechanisms.