Vapor-cell atomic clocks are compact and high-performance frequency references employed in various applications ranging from telecommunication to global positioning systems. Environmental sensitivities are often the main sources of long-term instabilities of the clock frequency. Among these sensitivities, the environmental pressure shift describes the clock frequency change with respect to the environmental pressure variations. We report here on our theoretical and experimental analysis of the environmental pressure shift on rubidium atomic frequency standards (RAFSs) operated under open atmosphere. By using an unsealed high-performance laser-pumped rubidium standard, we demonstrate that the deformation of the vapor-cell volume induced by the environmental pressure changes (i.e., barometric effect) is the dominant environmental pressure shift in a standard laboratory environment. An experimental barometric coefficient of /hPa is derived, in good agreement with theory and with previously reported measurements of frequency shifts of RAFS operated when transiting to vacuum.