A new type of acoustic metamaterials for ultrabroadband acoustic cloaking is proposed. Such metamaterials are constructed as grids consisting of nodes interconnected by sections of acoustic waveguides or links of other nature capable of transmitting longitudinal pressure waves. The nodes are thought of as cavities filled with an incompressible fluid. If the links are sufficiently short, such grids support plane pressure waves in the space of nodes, which approximates the physical space. The grids can be distorted under certain constraints so that the distortions do not affect the propagation in the space of nodes although the coordinates of nodes in the physical space are altered. This property of the proposed grids makes it possible to use them for constructing acoustic cloaks.