The classical theory of heat conduction (Fourier theory) predicts an infinite speed for thermal disturbance propagation, which is physically unrealistic. By extending the classical Fourier heat conduction and Fick's diffusion, this paper presents a hyperbolic diffusion law with different phase lags of thermal and moisture fluxes to simulate coupled heat-moisture diffusion-propagation behavior. Transient hygrothermal and elastic response of an infinitely long cylinder subjected to sudden hygrothermal loadings at the surface is studied. By using Laplace transform and decoupling technique, a closed form solution of temperature, moisture, displacements and stresses is determined. The analytical results show that the thermal and moisture relaxation times or phase lags of heat and moisture fluxes play a significant role in the early stage of transient response after heat/moisture shock. The classical results corresponding to vanishing phase lags can be recovered from the present ones. For non-vanishing phase lags, hygrothermal waves have finite propagation speeds. Numerical results are calculated and displayed graphically to show the influence of the phase lags of heat and moisture fluxes on transient hygrothermoelastic fields. A comparison between classic model and hyperbolic hygrothermal coupling model is given. Based on the non Fourier heat conduction and non-Fick diffusion, some shortcomings induced by the classical Fourier's and Fick's laws can be effectively avoided. (C) 2018 Elsevier Ltd. All rights reserved.