This paper investigates classification of submerged elastic targets using a sequence of backscattered acoustic signals corresponding to measurements at multiple target-sensor orientations. Wavefront and resonant features are extracted from each of the multiaspect signals using the method of matching pursuits, with a wave-based dictionary. A discrete hidden Markov model (HMM) is designed for each of the target classes under consideration, with identification of an unknown target effected by considering which model has the maximum likelihood of producing the observed sequence of feature vectors. HMMs are stochastic models which are well suited to describing piecewise-stationary processes, and are appropriate for multiaspect classification due to the strong aspect dependence of the scattered fields for most realistic targets. After establishing the physical and geometric correspondence between multiaspect sensing and the HMM parameters, performance is assessed through consideration of measured acoustic data from five similar submerged elastic targets. Results are presented with and without additive noise.