A series of laboratory model tests of a surface strip footing on air-dried sand was performed to evaluate the effects of the material viscosity of sand on the residual displacement characteristics of footing. The viscous deformation properties in the model tests were quantified in the framework of a non-linear three-component rheology model and compared with those from laboratory stress-strain tests. The following conclusions can be derived from the test results in this study; 1) significant effects of the material viscosity of the sand were observed on the footing pressure and footing settlement relation when the footing settlement rate was changed stepwise and sustained loading and load-relaxation tests were performed during otherwise monotonic loading tests on a model footing on air-dried sand. 2) the material viscous property of the model ground was quantified in terms of the rate-sensitivity coefficient, β, defined in the framework of a non-linear three-component model not as the Newtonian viscosity.