Three-dimensional　lattice　structures　with　high　specific　strength,　specific　stiffness　and　low　apparent　density,　are　widely　employed　across　multiple　engineering　fields.　Under　uniaxial　compressive　loading,　the　lattice　structure　may　experience　local　buckling　or　global　buckling.　This　paper　conducted　a　systematic　parametric　study　of　the　various　factors　affecting　the　buckling　behavior　of　multilayer　pyramid　lattice　structures　to　investigate　the　mechanism　of　the　two　main　instability　modes,　local　and　global　buckling.　It　was　found　that　the　critical　buckling　load　increases　with　the　increase　in　the　size　of　the　unit　cell　and　decreases　with　the　increase　in　the　total　height　of　the　structure　for　the　same　relative　density.　As　the　relative　density　increases,　the　buckling　resistance　of　the　lattice　structure　increases.　It　is　possible　to　examine　various　buckling　modes　by　varying　the　geometrical　properties　of　the　pyramid　unit　cell　(slenderness　ratio,　rod　inclination　angle,　cross-sectional　size　of　strut　connection　parts).　Finally,　numerical　simulations　were　performed　to　calculate　the　yield　strength　and　buckling　strength　of　the　lattice　structure　under　uniaxial　compression　load,　in　order　to　estimate　the　threshold　relative　density　for　structural　buckling　and　yield　failure.　The　results　demonstrated　that　buckling　failure　should　be　considered　for　aluminum　alloy　pyramid　lattice　when　the　relative　density　is　below　4.07%.　This　study　provides　design　criteria　for　lattice　structures　dominated　by　buckling　and　offers　ideas　for　improving　the　buckling　capacity　of　truss-type　lattice　structures.