The eigenvalue problem is analytically formulated in symmetric bridges with distributed mass and moment of inertia under transverse earthquake. The piers are elastically supported on the ground. The deck is monolithically connected to one or two piers for all degrees of freedom and restrained or transversely free at the abutments. The characteristic equation, symmetric normal modes, modal participation factors, and participating mass ratios are given analytically. The problem is expressed in terms of few dimensionless parameters: (i) the radius of gyration of the deck mass divided by the pier height; (ii) the ratio of the rotational stiffness of a footing to that of the pier at the base; (iii) the ratio of flexural stiffness of the outer spans to those of the pier; (iv) the ratio of torsional stiffness of side spans to the rotational stiffness of the pier top; (v) for two piers, the side-to-central-span ratio. Modal response spectrum analysis gives the moment at the base of the footings and the torque in the deck at its supports on the abutments as ratios to the values at incipient uplifting from the ground or the bearings. The peak ground acceleration of the motion at the onset of either one of these two types of nonlinearity is depicted as a function of the dimensionless parameters and the fundamental period of an elastic deck supported only at the abutments, or of a rigid deck on piers fixed against rotation at top and bottom.