Based on the Snyder-Mitchell model, with the method of separation of variables, exact analytical Hermite-Gaussian (HG) solutions are obtained in strongly nonlocal nonlinear media. The comparison of analytical solutions with numerical simulations of the nonlocal nonlinear Schrdinger equation (NNLSE) shows that the analytical HG solutions are in good agreement with the numerical simulations in the case of strong nonlocality. The evolution of the HG beam in strongly nonlocal nonlinear media is discussed. The results demonstrate that the width of the HG breathers vibrates periodically as they travel. Furthermore, the critical power for the soliton propagation, the solution of HG solitons, and the propagation constant are obtained. The critical power does not change with the mode number, and the propagation constant increases as the mode number increases. Gaussian breathers and Gaussian solitons can be treated as special cases of HG breathers and HG solitons.