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Shakedown (SD) and shape memory (SM) – generally looked upon as two different phenomena – are shown to have close relations from the point of view of their mechanisms, if considering the respective mesoscale processes on the one hand and the atomic scale processes on the other hand. With the use of the general mesomechanical concept of the first author, their constitutive equations are formulated using the same basic formulae, but with different meanings of the symbols. Constitutive equations are based on the description of internal stresses, in the case of SD on the mesoscale, in the case of SM on the atomic scale. Whereas in the case of SD, plastic deformation means shifting of atomic blocks and changing atomic neighbors, in the case of a diffusionless SM the atomic neighbors are maintained, what simplifies the analysis.