Purpose　This　study　aims　to　introduce　the　hybrid　finite　element　(FE)　-　meshfree　method　and　multiscale　variational　principle　into　the　traditional　mixed　FE　formulation,　leading　to　a　stable　mixed　formulation　for　incompressible　linear　elasticity　which　circumvents　the　need　to　satisfy　inf-sup　condition.　Design/methodology/approach　Using　the　hybrid　FE-meshfree　method,　the　displacement　and　pressure　are　interpolated　conveniently　with　the　same　order　so　that　a　continuous　pressure　field　can　be　obtained　with　low-order　elements.　The　multiscale　variational　principle　is　then　introduced　into　the　Galerkin　form　to　obtain　stable　and　convergent　results.　Findings　The　present　method　is　capable　of　overcoming　volume　locking　and　does　not　exhibit　unphysical　oscillations　near　the　incompressible　limit.　Moreover,　there　are　no　extra　unknowns　introduced　in　the　present　method　because　the　fine-scale　unknowns　are　eliminated　using　the　static　condensation　technique,　and　there　is　no　need　to　evaluate　any　user-defined　stability　parameter　as　the　classical　stabilization　methods　do.　The　shape　functions　constructed　in　the　present　model　possess　continuous　derivatives　at　nodes,　which　gives　a　continuous　and　more　precise　stress　field　with　no　need　of　an　additional　smooth　process.　The　shape　functions　in　the　present　model　also　possess　the　Kronecker　delta　property,　so　that　it　is　convenient　to　impose　essential　boundary　conditions.　Originality/value　The　proposed　model　can　be　implemented　easily.　Its　convergence　rates　and　accuracy　in　displacement,　energy　and　pressure　are　even　comparable　to　those　of　second-order　mixed　elements.