This chapter explores the geometric deformations of swallowtail and lips/beaks singularities. For the swallowtail singularity, the generic geometric deformations correspond to its \(\mathcal A\) -versal deformations. In these deformations, a single vertex appears on the discriminant, but no inflections are present. Lips/beaks singularities can exhibit infinitely many possible geometric deformations. This chapter focuses on the lips/beaks singularities that occur stably in generic one- or two-parameter families of map-germs from the plane to the plane—specifically, those of geometric codimension at most two. For lips singularities of geometric codimension one, there is a unique case of geometric deformation. In contrast, beaks singularities of the same codimension have two distinct cases, distinguished by the number of vertices that appear during deformation. Lips/beaks singularities of geometric codimension two are also examined in detail, with explicit descriptions of how inflections and vertices emerge, split, or disappear as the parameters vary.