This paper presents a theoretical analysis for predicting the initial stiffness and plastic collapse strength for micro-lattice structures under uniaxial compression or transverse shear loading. This theoretical analysis is based on the observed deformation mechanisms by numerical analysis, FEM, and can, in principle, be developed to predict the elastic properties of other micro-lattice structures. When the lattice structure is subjected to compression, the observed deformation pattern in a structure can be classified into three types. Also, when the structure is subjected to shear load, the deformation pattern observed in the structure can be classified into two types. The theoretical results for each deformation pattern are proposed based on the classical beam theory, and show good agreement with numerical results obtained by FEM.