Due to physiological structure of most of the soft biological tissues, measurable stresses develop after the specimen has been stretched to many hundreds of percent of its relaxed length. Therefore, the nonlinear stress-strain relations developed for vulcanized rubber cannot be applied to soft tissues, which are constitutionally much more nonlinear than other engineering materials. In this article, using two different elastic models proposed for elastic soft tissues, simple elongation of a cylindrical bar and the inflation of a spherical thick shell, which is deemed to be a model for a left venticle, are studied and the material coefficients characterizing the elastic model are obtained via comparing theoretical results with existing experiments on tissues. Furthermore, the elastic stiffnesses which are very important for physiologists and cardiologists are discussed and the consistency of the result with experiments are indicated.