Photoacoustic computed tomography (PACT) holds great promise for transcranial brain imaging. However, the strong reflection, scattering and attenuation of acoustic waves in the skull present significant challenges to developing this method. We report on a systematic computer-simulation study of transcranial brain imaging using PACT. The goal of this study was to identify an effective imaging system design that can be translated for clinical use. The propagation of photoacoustic waves through a model skull was studied by use of an elastic finite-difference time-domain (FDTD) method. The acoustic radiation pattern from a photoacoustic source just beneath the skull was observed with a ring transducer array that was level with the source. The observed radiation pattern was found to contain stronger contributions from waves that were converted to shear waves in skull than longitudinal waves that did not undergo mode conversion. Images reconstructed from the pressure data that contain shear wave components possess better resolution than images reconstructed from the data that only contain the longitudinal wave signals. These observations revealed that the detection system should be designed to capture photoacoustic signals that travel through the skull in the form of shear waves as well as in the form of longitudinal waves. A preliminary investigation on the effect of the presence of absorption in the skull is also reported. This study provides an insight into the wave phenomena in transcranial PACT imaging, as well as a concrete detection design strategy that mitigates the degraded resolution of reconstructed images.