Although rubber is capable of very large elastic deformation, it also shows significant viscoelastic behavior and a strain-induced, stress-softening phenomenon (the Mullins effect). In this paper, tensile, planar tension and equal biaxial cyclic tests are used to study the viscoelastic and stress-softening effects of rubbers and a numerical method is proposed to evaluate the stress relaxation function and the model parameters of constitutive equations from the cyclic tests. The Arruda-Boyce model is used to fit the cyclic tests. The Mullins effect is evaluated by assuming the model parameters of the Arruda-Boyce model to be a function of the maximum first strain invariant in the prior loading history. A carbon black-filled fluoroelastomer is studied with the proposed method. The results show that the stress relaxation function obtained from the stress relaxation test differs from that obtained from the cyclic tests. In addition, the scaling coefficient method used in most commercial finite element codes to model the Mullins effect is also investigated.