S U M M A R YWe propose a new approach for the inversion of anisotropic P-wave data based on Monte Carlo methods combined with a multigrid approach. Simulated annealing facilitates objective minimization of the functional characterizing the misfit between observed and predicted traveltimes, as controlled by the Thomsen anisotropy parameters (ε, δ). Cycling between finer and coarser grids enhances the computational efficiency of the inversion process, thus accelerating the convergence of the solution while acting as a regularization technique of the inverse problem. Multigrid perturbation samples the probability density function without the requirements for the user to adjust tuning parameters. This increases the probability that the preferred global, rather than a poor local, minimum is attained. Undertaking multigrid refinement and Monte Carlo search in parallel produces more robust convergence than does the initially more intuitive approach of completing them sequentially. We demonstrate the usefulness of the new multigrid Monte Carlo (MGMC) scheme by applying it to (a) synthetic, noise-contaminated data reflecting an isotropic subsurface of constant slowness, horizontally layered geologic media and discrete subsurface anomalies; and (b) a crosshole seismic data set acquired by previous authors at the Reskajeage test site in Cornwall, UK. Inverted distributions of slowness (s) and the Thomson anisotropy parameters (ε, δ) compare favourably with those obtained previously using a popular matrix-based method. Reconstruction of the Thomsen ε parameter is particularly robust compared to that of slowness and the Thomsen δ parameter, even in the face of complex subsurface anomalies. The Thomsen ε and δ parameters have enhanced sensitivities to bulk-fabric and fracture-based anisotropies in the TI medium at Reskajeage. Because reconstruction of slowness (s) is intimately linked to that ε and δ in the MGMC scheme, inverted images of phase velocity reflect the integrated effects of these two modes of anisotropy. The new MGMC technique thus promises to facilitate rapid inversion of crosshole P-wave data for seismic slownesses and the Thomsen anisotropy parameters, with minimal user input in the inversion process.Subsurface media commonly exhibit seismic anisotropy, caused for example by changes in lithology or stratigraphy, the intensity and pattern of fracturing, preferred mineral alignment or mechanical or fluid processes. It is well known that failure to account for anisotropy can lead to significant errors in tomographic reconstructions of * Formerly at: School of Planning, Architecture, and Civil Engineering, Queen's University Belfast, Belfast BT9 5AG, UK. subsurface slowness using compressional (P-) wave data (Carrion et al. 1992). The Thomsen (1986) parameters (ε, δ), are useful measures of anisotropically propagating P wave fronts in weakly anisotropic media (∼10-20 per cent)