We consider singularities of frontal surfaces of corank one and finite frontal codimension. We look at the classification under A -equivalence and introduce the notion of frontalisation for singularities of fold type. We define the cuspidal and the transverse double point curves and prove that the frontal has finite codimension if and only if both curves are reduced. Finally, we also discuss about the frontal versions of the Marar-Mond formulas and the Mond's conjecture.