Lung epithelial cells are subjected to large cyclic forces from breathing. However, their response to dynamic stresses is poorly defined. We measured the complex shear modulus (G*(ω)) of human alveolar (A549) and bronchial (BEAS-2B) epithelial cells over three frequency decades (0.1–100 Hz) and at different loading forces (0.1–0.9 nN) with atomic force microscopy. G*(ω) was computed by correcting force-indentation oscillatory data for the tip-cell contact geometry and for the hydrodynamic viscous drag. Both cell types displayed similar viscoelastic properties. The storage modulus G′(ω) increased with frequency following a power law with exponent ∼0.2. The loss modulus G″(ω) was ∼2/3 lower and increased similarly to G′(ω) up to ∼10 Hz, but exhibited a steeper rise at higher frequencies. The cells showed a weak force dependence of G′(ω) and G″(ω). G*(ω) conformed to the power-law model with a structural damping coefficient of ∼0.3, indicating a coupling of elastic and dissipative processes within the cell. Power-law behavior implies a continuum distribution of stress relaxation time constants. This complex dynamics is consistent with the rheology of soft glassy materials close to a glass transition, thereby suggesting that structural disorder and metastability may be fundamental features of cell architecture.