The paper deals with radial compress wave propagation in 2D continuum, the density of which is a continuous random function of (x,y) coordinates. This concept refers materials with microscopic non-homogeneity. Many papers appeared dealing with similar problem in a semi-infinite bar (1D) using spectral decomposition or Fokker-Planck equation analysis. Harmonic excitation acts in the origin. Material density is considered as a sum of a constant mean value and Gaussian, homogeneous and ergodic material density fluctuations in a plane (x,y). The correlation function is approximated as exponential being dependent on the distance of two points only. Derived spectral density in polar coordinates reads then in Bessels functions. The governing integro-differential system transformed into Fokker-Planck equation for unknown stochastic parameters of waves propagating from the origin is then investigated. There has been shown a steep drop of the response deterministic part due to material stochastic character and a simultaneous increase of the response uncertainty (stochastic part) with the ascending distance from the point of excitation. These processes don't represent any mechanical energy los, but only changes of its form. An upper limit of the excitation frequency (critical frequency) depending on the mean correlation length of material imperfections has been identified.