Measurements of lithium (Li) abundances in solar-type stars have shown that standard models of stellar evolution are incapable of explaining the observed depletion as a function of stellar age. Beryllium (Be) is one of the lightest elements that can be measured in stellar photospheres and can be burned at relatively low temperatures. Studying its abundances as a function of stellar age can provide important constraints to stellar mixing models because the level of depletion as a function of time will indicate how deep the photospheric material must be dredged to explain the observed abundances. In an effort to provide the most stringent constraints for nonstandard stellar mixing models, we observed a sample of solar twins and concomitantly analyzed their Li and Be abundances. Unlike what is typically observed for Li, we found that Be does not decrease as a function of stellar age along the main sequence, constraining models that predict the burning of both materials. Based on our data, models that invoke convective overshoot and convective settling are preferred over typical rotationally induced mixing models, as the later burn Be in excess while the former do not. Previous works also proposed mixing due to gravity waves as a possible explanation for observed abundances, which can fit our data as well. Furthermore, based on our solar twins, Be depletion likely happens within the first similar to 1 Gyr. We also confirm previous findings of an increase in Be abundance as a function of metallicity, indicative of galactic production via cosmic-ray spallation.