Most current seismic codes take account of the effect of uncertainty in the in-plan distribution of mass introducing an accidental eccentricity, which is generally equal to 5% of the length of the deck of the building. The same codes, instead, do not account for the uncertainty in the distribution of mass along the height of the building. This paper verifies whether the in-elevation irregularity promoted by the uncertainty in the distribution of mass can be neglected with specific regard to steel concentrically braced frames in the chevron configuration. To this end, two 8-story concentrically braced frames are first designed assuming a distribution of mass that is constant along the height. Multiple stripe analyses are then carried out on numerical models with either uncertain or median properties of loads and mass. The performances of the structures are determined in terms of mean annual frequency of exceedance of Damage Limitation, Significant Damage and Near Collapse limit states. Further, attention is focused on the heightwise distribution of drifts and local response parameters achieved for prefixed values of the selected intensity measure.