Experimental data are reported on isotactic polypropylene in uniaxial tensile cyclic tests with a strain-controlled program (oscillations between fixed minimum and maximum strains). The following characteristic features of stressstrain diagrams are observed: (i) logarithmic decay in maximum and minimum stresses with number of cycles (cyclic softening), (ii) more pronounced reduction in minimum stress than in maximum stress (cyclic strengthening), (iii) independence of rates of decrease in maximum and minimum stresses of strain rate, (iv) decrease in hysteresis energy with number of cycles. To rationalize these observations, a constitutive model is derived in cyclic viscoelasticity and viscoplasticity of semicrystalline polymers. Numerical simulation demonstrates that the model correctly describes experimental stressstrain curves and quantitatively predicts evolution of maximum and minimum stresses with number of cycles. POLYM. ENG. SCI., 2012. (C) 2012 Society of Plastics Engineers