Abstract: A novel high-order spring-dashpot-mass model (SDMM) forconvolution integral of force-displacement relationship in time domain isproposed and applied into the cylindrical-symmetry wave motions in infinitedomain as an artificial boundary condition (ABC). First, the high-order SDMMis dynamically and numerically stable, while low- and high-frequencyinstabilities occur under the displacement-type ABCs in term of space-timeextrapolation, such as multi-transmitting formula (MTF) and Pad\'eboundary. Second, SDMM has higher numerical accuracy thanthe stress-type ABCs, such as viscous boundary (VB) and viscous-springboundary (VSB). Third, SDMM is strictly doubly asymptotic at low- andhigh-frequency limits, and can be degenerated to VB or VSB. Fourth, SDMM canbe incorporated simply and easily into commercial FE software by using theinternal spring-dashpot and mass elements and time-integration solvers.Several numerical cases were carried out to validate the particular featuresof SDMM.