Shakedown theory for elastic-perfectly plastic solids is represented in a consistent manner. Admissible residual stresses of the static theorem are required to be bounded. Fictitious material, which can yield in bulk tension and compression, is used for constructing the shakedown kinematic theorem. The new formulation has an advantage for possible practical numerical implementation. It does not require the compatible end-cycle plastic strain increment for shakedown analysis to be deviatoric a priori. Moreover, simple estimates for the rotating plastic collapse loads are deduced, which provide some possible different modes: alternating plasticity, local rotating plasticity, and global rotating plasticity, the last one is caused by the compatibility restrictions for the strains on the whole body in addition to the variation of the stresses.