  In this paper we derive a model to describe the important inelastic features
associated with the cyclic softening, often referred to as stress-softening, of
soft biological tissue. The model developed here includes the notion of
multiple stress-strain cycles with increasing values of the maximum strain. The
model draws upon the similarities between the cyclic softening associated with
carbon-filled rubber vulcanizates and soft biological tissue. We give
non-linear transversely isotropic models for the elastic response, stress
relaxation, residual strain and creep of residual strain. These ideas are then
combined with a transversely isotropic version of the Arruda-Boyce eight-chain
model to develop a constitutive relation that is capable of accurately
representing the multicyclic softening of soft biological tissue. To establish
the validity of the model we have compared it with experimental data from three
cyclic uniaxial test samples, one taken from the \textit{Manduca sexta}
(tobacco hornworm) caterpillar and the other two samples taken from the human
aorta, one in the longitudinal and the other in the circumferential direction.
The model was found to fit these experimental data extremely well. {Keywords:}
Mullins effect, stress relaxation, creep of residual strain, biological tissue,
transverse isotropy. {MSC codes:} 74B20, 74D10, 74L15, 92C10
