Equicontinuity plays a vital role in general metric spaces and multiple studies have tried to characterize equicontinuity since its origin. Advent of soft set theory leads us to study these mappings in terms of soft sets, as well. In this paper, first we introduce the concept of soft equicontinuity, soft pointwise equicontinuity and soft uniform equicontinuity with examples. Moreover, we explore soft continuity of soft pointwise limit of a sequence of soft mappings when the family of the given soft mapping is a soft equicontinuous mapping and then discuss soft pointwise convergence of sequence of soft mappings which are a soft pointwise equicontinuous mappings when co-domain is soft complete space. We also give characterizations of soft pointwise equicontinuity and soft uniform equicontinuity in terms of convergent sequence of soft points in soft dense subset