Abstract: Interval Bézier surfaces are introduced based on the interval analysis.Two algorithms for approximating non-rational and rational surface by interval Bézier surfaces are given. Applications of approximating these two types of surfaces by interval Bézier polynomial surface are presented.Then the boundaries of interval Bézier surfaces are investigated.It is proved that the boundary of degree m ×n interval Bézier surface is made up from piecewise degree m ×n trimmed Bézier patches，ruled surface patches with generating lines parallel to coordinate axis， and rectangular plane patches parallel to coordinate planes.