Current clinical ultrasound scanners cannot be used to image the interior morphology of bones because these scanners fail to address the complicated physics involved for exact image reconstruction. Here, we show that if the physics is properly addressed, bone cortex can be imaged using a conventional transducer array and a programmable ultrasound scanner. We provide in vivo proof for this technique by scanning the radius and tibia of two healthy volunteers and comparing the thickness of the radius bone with high-resolution peripheral x-ray computed tomography. Our method assumes a medium that is composed of different homogeneous layers with unique elastic anisotropy and ultrasonic wave-speed values. The applicable values of these layers are found by optimizing image sharpness and intensity over a range of relevant values. In the algorithm of image reconstruction we take wave refraction between the layers into account using a ray-tracing technique. The estimated values of the ultrasonic wave-speed and anisotropy in cortical bone are in agreement with ex vivo studies reported in the literature. These parameters are of interest since they were proposed as biomarkers for cortical bone quality. In this paper we discuss the physics involved with ultrasound imaging of bone and provide an algorithm to successfully image the first segment of cortical bone.