We present noble gas data for 16 shergottites, 2 nakhlites (NWA 5790, NWA 10153), and 1 angrite (NWA 7812). Noble gas exposure ages of the shergottites fall in the 1–6 Ma range found in previous studies. Three depleted olivine‐phyric shergottites (Tissint, NWA 6162, NWA 7635) have exposure ages of ~1 Ma, in agreement with published data for similar specimens. The exposure age of NWA 10153 (~12.2 Ma) falls in the range of 9–13 Ma reported for other nakhlites. Our preferred age of ~7.3 Ma for NWA 5790 is lower than this range, and it is possible that NWA 5790 represents a distinct ejection event. A Tissint glass sample contains Xe from the Martian atmosphere. Several samples show a remarkably low (21Ne/22Ne)cos ratio < 0.80, as previously observed in a many shergottites and in various other rare achondrites. This was explained by solar cosmic ray‐produced Ne (SCR Ne) in addition to the commonly found galactic cosmic ray‐produced Ne, implying very low preatmospheric shielding and ablation loss. We revisit this by comparing measured (21Ne/22Ne)cos ratios with predictions by cosmogenic nuclide production models. Indeed, several shergottites, acalpulcoites/lodranites, angrites (including NWA 7812), and the Brachina‐like meteorite LEW 88763 likely contain SCR Ne, as previously postulated for many of them. The SCR contribution may influence the calculation of exposure ages. One likely reason that SCR nuclides are predominantly detected in meteorites from rare classes is because they usually are analyzed for cosmogenic nuclides even if they had a very small (preatmospheric) mass and hence low ablation loss.