Photoacoustic computed tomography (PACT) is an emerging computed imaging modality that exploits optical contrast and ultrasonic detection principles to form images of the photoacoustically induced initial pressure distribution within tissue. The PACT reconstruction problem corresponds to a time-domain inverse source problem, where the initial pressure distribution is recovered from the measurements recorded on an aperture outside the support of the source. A major challenge in transcranial PACT of the brain is to compensate for aberrations and attenuation in the measured data due to the propagation of the photoacoustic wavefields through the skull. To properly account for these effects, a wave equation-based inversion method can be employed that can model the heterogeneous elastic properties of the medium. In this study, an optimization-based image reconstruction method for 3D transcranial PACT is developed based on the elastic wave equation. To accomplish this, a forward-adjoint operator pair based on a finite-difference time-domain discretization of the 3D elastic wave equation is utilized to compute penalized least squares estimates of the initial pressure distribution. Computer-simulation and experimental studies are conducted to investigate the robustness of the reconstruction method to model mismatch and its ability to effectively resolve cortical and superficial brain structures.