Abstract：Natural slopes appearing secondary creep phenomenon under natural conditions，such as storm， rainfall，and flow-erosion，are discussed. In addition，slope initial stress changes caused by human activities to arise secondary creep phenomenon are also analyzed. Then，the visco-elastic creep compliance solution is proposed，which gives a new elastic displacement formula and simplifies the relationships between elasticity theory and visco-elasticity theory. The applications of these two theories are illustrated by secondary creep phenomenon of slope. That means visco-elastic displacement analytic solution can be achieved through elastic displacement analytic solution. Based on horizontal plane slope which is proposed by Goodman，simple analytic solution of visco-elastic displacement for algebraic transformation of mechanical parameter，five different analytic solutions of visco-elastic creep compliance，and generalized creep compliance，are introduced. The five different constitutive relations of horizontal plane slope visco-elastic displacement analytic solution are achieved.
