Tetrahedral　lattice　materials　can　be　used　as　the　core　of　a　sandwich　structure.　The　properties　of　tetrahedral　lattice　materials　can　be　controlled　by　modifying　their　geometrical　parameters　and　relative　density.　In　this　paper,　a　tetrahedral　lattice　structure　deformation　mechanism-based　theoretical　analysis　model　is　established　to　predict　the　effective　mechanical　properties　of　the　structure　under　compressive　and　shear　loadings.　The　analytical　solutions　are　subsequently　verified　by　finite　element　analysis　of　a　large-scale　lattice　material　model.　Based　on　the　obtained　results,　the　effects　of　the　geometrical　parameters,　relative　density,　and　shear　deformation　are　discussed.　At　a　specific　relative　density,　as　strut　inclination　angle　increases:　(1)　the　effective　compressive　modulus　in　the　z-direction　increases;　(2)　the　effective　compressive　modulus　in　x-　and　y-directions,　and　the　effective　shear　modulus　in　xy-,　xz-,　and　yz-directions　firstly　increases　but　then　decreases;　(3)　the　effective　Poisson＇s　ratios　νzx　and　νzy　increase,　whereas,　νxz,　νyz,　νxy,　and　νyx　decrease.　With　an　increase　in　relative　density,　the　effective　compressive　and　shearing　modulus　increase,　the　effective　Poisson＇s　ratios　remain　constant,　νxy　and　νyx　are　always　equal　to　0　when　the　strut　inclination　angle　is　45°.　The　effect　of　shear　deformation　on　the　effective　mechanical　properties　increases　as　the　slenderness　ratio　increases.　The　predicted　effective　properties　enable　the　tetrahedral　lattice　unit　cells　to　be　treated　as　＂material＂in　the　design　and　analysis　process.　　©　2023　World　Scientific　Publishing　Europe　Ltd.