The myocardium of the left ventricle (LV) of the heart comprises layers of muscle fibers whose orientation varies through the heart wall. Because of these fibers, accurate modeling of the myocardium stress-strain behavior requires models that are nonlinear, anisotropic, and time-varying. This article describes the development and testing of a material model of the canine LV myocardium, which will be used in ongoing simulations of the mechanics of the LV with fluid-structure interaction. The model assumes that myocardium deformation has two extreme states: one during which the muscle fibers are fully relaxed, and another during which the muscle fibers are fully contracted. During the second state, the “total” stresses are assumed to be the sum of “passive” stresses, which represent the fully relaxed muscle fibers, and “active” stresses, which are additional stresses due to the contraction of the muscle fibers. The canine LV myocardium is modeled as a transversely isotropic material for which material properties vary in the fiber and cross-fiber directions. The material behavior is considered to be hyperelastic and is modeled by a strain-energy density function in a manner that is an adaptation of an approach based on measurements of the stress-strain behavior of rabbit LV myocardia. A numerical method has been developed to calculate suitable parameter values for the passive material model using previous passive canine LV myocardium stress measurements and taking into account existing physical and numerical constraints. In the absence of published measurements of total canine LV myocardium stresses, a method has been developed to estimate these stresses from available passive and total rabbit LV myocardium stresses and then to calculate active material parameter values. Material parameter values were calculated for passive and active canine LV myocardium. Passive stresses calculated using the model compare well to previous stress measurements while active stresses calculated using the model compare well with those approximated from rabbit measurements. The adapted material model of the canine LV myocardium is deemed to be suitable for use in simulations of the operation of both idealized and realistic canine hearts. The estimated model parameter values can be easily revised to more appropriate ones if measurements of active canine LV myocardium stresses become available. The extension of this material model to a fully orthotropic one is also possible but determination of its parameters would require stress-stretch measurements in the fiber and both cross-fiber directions.