The strain effects on the intercalation potentials of LiMnO2 and Li2MnO3 are investigated by the first principles method, and the relationship between the intercalation potential and the strain is given in the form of elastic response. All the modes of strain reduce the intercalation potential and the effect is anisotropic. Most of the single modes reduce the potential by less than 0.1 V when the strains are 5%. The bonding between the host layers is rather sensitive to the strain perpendicular to the host layer when the lithium vacancy left by lithium extraction is in the lithium layer, thus that strain brings more reduction to the intercalation potential; whereas for the Li2MnO3 system when lithium is extracted form the transition metal layer, the strain along the host layer brings more reduction to the potential. For the Li2MnO3-stabilized LiMO2 (M=Mn, Ni, Co) solid solution system, the strain can keep the voltage of the high potential charging stage lower than the cut-off voltage, and open up the migrating pathway of lithium in the transition metal layer, therefore the charging can last a long time and larger charging capacity is achieved.