New R- and B(J) band images of the gravitational lens 0957 + 561 show a pair of elongated blue objects 20'' from the lens center; their morphology strongly suggests that they are distorted images of background galaxies, and as such they place new constraints on models of this lens system. The implications for the Hubble constant and for the mass distribution in the lens are investigated using a variety of parametric models. The models of Falco et al. [ApJ, 310, 568 (1991)] and of Kochanek [ApJ 382, 58 (1991)] cannot describe the observed arcs. Lenses consisting of an isothermal galaxy (G1) and softened-core isothermal cluster cannot form the arc for velocity dispersions comparable to those observed. Models in which the mass of the galaxy traces its light also fail without the addition of a third strong deflector. Galaxy mass profiles of nonisothermal power laws can produce the arc, but only if the lens is marginal, G1 has low mass, and therefore the implied value of H0 is below 32. Inclusion of a mass of order 10(14) M. at the location of the z = 0.5 group of galaxies in the field allows a new branch of solutions with higher galaxy masses, cluster masses consistent with the measured velocity dispersions, and values of H0 up to 68. The further addition of a constant shear to the lens model allows the Hubble constant to be as large as 87. These models satisfy all of the lensing constraints, agree with the locally determined distance scale, and have masses consistent with all existing dynamical estimates. Further observation of the system should differentiate between the low-H0 and high-H0 sets of solutions. Surface photometry of the outer portions of the lens galaxy G1 show that it is well fit by a deVaucouleurs profile with r(e) almost-equal-to 14h-1 kpc and m(R) almost-equal-to 17.0, and is a typical brightest cluster elliptical. If the high-H0 models are correct, then the galaxy mass profile is at least as steep as isothermal, perhaps as steep as mass traces light.