Recently,　flexible　electrodes　with　biaxial/omnidirectional　stretchability　have　attracted　significant　attention.　However,　most　existing　pliable　electrode　materials　can　be　only　stretched　in　one　direction.　In　this　work,　an　unexpected　isotropic　van　der　Waals　(vdW)　heterostructure　is　proposed,　based　on　the　assembly　of　two-dimensional　crystals　of　anisotropic　black　phosphorene　(BP)　and　transition　metal　carbide　(TiC2).　Using　vdW-corrected　density　functional　theory　calculations,　the　BP/TiC2　vdW　heterostructure　was　predicted　to　have　excellent　structural　and　mechanical　stability,　superior　electrical　conductivity,　omnidirectional　flexibility,　and　a　high　Li　storage　capacity.　We　have　unraveled　the　physical　origin　of　the　excellent　stability,　as　well　as　the　Li　adsorption　preferences　of　the　lithiated　heterostructure,　based　on　a　three-step　analysis　of　the　stability　of　the　Li-adsorption　processes.　In　addition,　the　BP/TiC2　vdW　heterostructure　can　also　be　applied　as　the　anode　material　for　flexible　Na-ion　batteries　because　of　its　high　Na　storage　capacity　and　strong　Na　binding.　However,　compared　with　Na　adsorption,　the　capacity　is　higher,　and　the　adsorption　energy　is　more　negative　for　Li　adsorption.　Our　findings　provide　valuable　insights　into　the　exploration　of　a　rich　variety　of　vdW　heterostructures　for　next-generation　flexible　energy　storage　devices.　[Figure　not　available:　see　fulltext.].　©　2017,　Tsinghua　University　Press　and　Springer-Verlag　Berlin　Heidelberg.