We propose a numerical and an experimental study of an invisibility carpet for linear water waves. In the first part, we introduce the concept of an invisibility carpet in the case of linear water waves and apply this concept for a bounded problem: a wavetank. In the second part, we study a simpler case where we attempt to render invisible a vertical dihedral at the end of a wavetank. This is done by placing a structure consisting of 18 vertical poles with trapezoidal cross-sections in front of the dihedral. For these two configurations, with and without the carpet, we focus on the far-field reflected wave consisting of an inline mode and the first sloshing (plus progressive) mode. We show that our design achieves invisibility.