The reliable estimation of the wavenumber space (k-space) of the plates remains a long-term concern for acoustic modeling and structural dynamic behavior characterization. Most current analyses of wavenumber identification methods are based on the deterministic hypothesis. To this end, an inverse method is proposed for identifying wave propagation characteristics of two-dimensional structures under stochastic conditions, such as wavenumber space, dispersion curves, and band gaps. The proposed method is developed based on an algebraic identification scheme in the polar coordinate system framework, thus named Algebraic K-Space Identification (AKSI) technique. Additionally, a model order estimation strategy and a wavenumber filter are proposed to ensure that AKSI is successfully applied. The main benefit of AKSI is that it is a reliable and fast method under four stochastic conditions: (A) High level of signal noise; (B) Small perturbation caused by uncertainties in measurement points’ coordinates; (C) Non-periodic sampling; (D) Unknown structural periodicity. To validate the proposed method, we numerically benchmark AKSI and three other inverse methods to extract dispersion curves on three plates under stochastic