  Inspired by the concept of evolutoids of planar curves, we present the
concept of evolutoids for regular surfaces as an envelope of a two-parameter
family of lines in Euclidean 3-space. We give an explicit parametrization for
such evolutoids. Besides, we used the theory of singularities to study the
local behavior of regular points of this object and presented some relations
between the geometry of the regular surface and its evolutoid.
