The failure of grid structures with periodic and quasi-periodic designs under uniaxial compression is investigated. The quasi-periodic cellular structure is built on the principles of biomimicry. Structures characteristic of living nature are used as a prototype. A honeycomb is the prototype for the periodic structure, and the quasiperiodic structure is built with regard to the geometric principles of the skeleton of Aphrocallistes sp. (a sea sponge). It has been found that there is a 24 % increase in effective work spent on the first act of the failure of the object with uniaxial compression in structures with elementary components - imperfect elements that distinguish them from hexagons (the angle between the sides, the size and shape of the cells). The correlation of the failure pattern of the grid structures with periodic and quasiperiodic designs to the amount of work spent on the complete failure of the samples has been established. It has been revealed that, for the samples with a periodic structure, the first act of failure is characterized by the main failure of the intermodal membranes along the entire perimeter, i.e. that it is one-dimensional sequential annular failure. The samples with a quasi-periodic structure are characterized by two-dimensional failure, i.e., for the load-bearing capacity of an object to be significantly reduced, there must be a greater number of destroyed intermodal membranes per unit area and, therefore, a higher density of destroyed elements.