The design of engineered wood products and timber structures involving numerical simulations requires knowledge of the elastic and strength properties of wood. This study characterized the elastic behavior of Uruguayan pine wood (Pinus elliottii and P. taeda). A series of compression tests with the load applied with respect to various grain directions and bending tests were performed on small and clear specimens to determine the elastic constants and establish the relationships between the longitudinal moduli of elasticity obtained by the two testing methods. Moduli of elasticity, shear moduli, and Poisson ratios were determined. The longitudinal stiffness values in compression from the same specimen obtained by the two testing methods were similar. The moduli of elasticity in tension and compression parallel to the grain for the elastic behavior was obtained from experimental bending tests, and the downshift of the neutral axis until rupture was found. Using a model that simulates the post-elastic behavior as a curve comprised of several straight lines, the stress-strain diagram for tension and compression parallel to the grain was obtained.