The pillow is a defect that adversely affects the geometrical accuracy as well as the formability in single-point incremental forming. With a main objective to control this defect, the effects of mechanical properties of material on pillowing are examined in this work. To identify the mechanical property that significantly affects pillowing, single-point incremental forming tests are conducted using a variety of materials (i.e. 11). It is found that a property (i.e. area reduction at tensile fracture) that controls the formability of a material in single-point incremental forming does not have any significant effect on its pillowing tendency. Interestingly, hardening exponent (i.e. a property that has controlling influence on the stretch-ability of material) appears to be the most influential property that determines the pillowing tendency of sheet metals in single-point incremental forming. Furthermore, the pillowing tendency of a material decreases with the decrease in this particular property. This, according to finite element analysis, occurs because strain localization around the tool/sheet contact correspondingly increases. To select and rank materials with respect to the pillowing behavior, a formula describing the property–pillowing relationship is proposed. As a secondary objective, the correlation between pillowing and forming depth is also investigated in this work. It is shown that initially the pillow progresses as the forming depth increases. However, after forming has been carried out to a certain depth, the pillow begins to regress, most likely due to strain hardening of sheet metal. In conclusion, it is suggested to lower the hardening exponent of sheet metals in order to control pillowing in single-point incremental forming.