We present a monolithic mechanical metamaterial comprising a periodic arrangement of snapping units with tunable tensile behavior. Under tension, the metamaterial undergoes a large extension caused by sequential snap-through instabilities, and exhibits a pattern switch from an undeformed wavy-shape to a diamond configuration. By means of experiments performed on 3D printed prototypes, numerical simulations and theoretical modeling, we demonstrate how the snapping architecture can be tuned to generate a range of nonlinear mechanical responses including monotonic, S-shaped, plateau and non-monotonic snap-through behavior. This work contributes to the development of design strategies that allow programming nonlinear mechanical responses in solids.