Fibrolamellar bone is a transient primary bone tissue found in fast-growing juvenile mammals, several species of birds and large dinosaurs. Despite the fact that this bone tissue is prevalent in many species, the vast majority of bone structural and mechanical studies are focused on human osteonal bone tissue. Previous research revealed the orthotropic structure of fibrolamellar bone, but only a handful of experiments investigated its elastic properties, mostly in the axial direction. Here we have performed for the first time an extensive biomechanical study to determine the elastic properties of fibrolamellar bone in all three orthogonal directions. We have tested 30 fibrolamellar bone cubes (2 × 2 × 2 mm) from the femora of five juvenile white-tailed deer (Odocoileus virginianus) in compression. Each bone cube was compressed iteratively, within its elastic region, in the axial, transverse and radial directions, and bone stiffness (Young's modulus) was recorded. Next, the cubes were kept for 7 days at 4 °C and then compressed again to test whether bone stiffness had significantly deteriorated. Our results demonstrated that bone tissue in the deer femora has an orthotropic elastic behavior where the highest stiffness was in the axial direction followed by the transverse and the radial directions (21.6 ± 3.3, 17.6 ± 3.0 and 14.9 ± 1.9 Gpa, respectively). Our results also revealed a slight non-significant decrease in bone stiffness after 7 days. Finally, our sample size allowed us to establish that population variance was much bigger in the axial direction than the radial direction, potentially reflecting bone adaptation to the large diversity in loading activity between individuals in the loading direction (axial) compared with the normal (radial) direction. This study confirms that the mechanically well-studied human transverse-isotropic osteonal bone is just one possible functional adaptation of bone tissue and that other vertebrate species use an orthotropic bone tissue structure which is more suitable for their mechanical requirements.