PAMs mimic behavior of skeletal muscles by generating contractile force in a nonlinear way when they are pressurized. Due to the non-linear mechanical behavior of elastomers, stiffness of these actuators would depend on the applied pressure. Therefore, it is important to obtain a precise mechanical model for them. In this work, based on the theory of limiting chain extensibility (LCE), a new continuum mechanics-based model is developed for elastomeric pneumatic artificial muscles to predict stiffness and output parameters such as free contraction, blocked force and dead-band pressure actuation course. The developed model is consistent to the network alternation theories which gives the opportunity to predict the Mullins softening occurred in the first cycles of inflation-deflation.