s-dense monomorphisms and injectivity with respect to these monomorphisms were first introduced and studied by Giuli for acts over the monoid (N1, min). Ebrahimi, Mahmoudi, Moghaddasi, and Shahbaz generalized these notions to acts over a general semigroup. In this paper, we study flatness with respect to the class of s-dense monomorphisms. The theory of flatness properties of acts over monoids has been of major interest over the past some decades, but so far there are not any papers published on this subject that relate specifically to the class of s-dense monomorphisms. We give some suficient conditions for s-dense flatness of semigroup acts. Also, we characterize a large number of semigroups over which s-dense flatness coincides with flatness. This gives a useful criterion for flatness of acts over such semigroups. In fact it is shown that the study of s-dense flatness is also useful in the study of ordinary flatness of acts.