Transferring completed electronic devices onto curvilinear surfaces is popular for fabricating three-dimensional curvilinear electronics with high performance, while the problems of conformality between the unstretchable devices and the surfaces need to be considered. Prior conformability design based on conformal mechanics model is a feasible way to reduce the non-conformal contact. Former studies mainly focused on stretchable film electronics conforming onto soft bio-tissue with a sinusoidal form microscopic morphology or unstretchable film conforming onto rigid sphere substrate, which limits its applicability in the aspect of shapes and modulus of the substrate. Here, a conformal mechanics model with general geometric shape and material is introduced by choosing a bicurvature surface as the target surface, and the conformal contact behavior of film electronics is analyzed. All eight fundamental local surface features are obtained by adjusting two principal curvatures of the bicurvature surface, and the conformal performance is simulated. A dimensionless conformal criterion is given by minimizing the total energy as a function of seven dimensionless parameters, including four in geometric and three in the material. Thickness–width ratio and length–width ratio of flexible electronics are two key geometric parameters that decide the conformal behavior, and smaller thickness–width ratio and length–width ratio are favorite for conformal contact. The model and analysis results are verified by the finite element analysis, and it can guide the prior conformability design of the curvilinear electronic devices during the planar manufacturing process.