Summary: The paper provides weighted Sobolev inequalities of the Caffarelli-Kohn-Nirenberg type for functions with multi-radial symmetry. An elementary example of such inequality is the following inequality of Hardy type for functions \(u=u(r_1(x),r_2(x))\), where \(r_1(x)=\sqrt{x_1^2+x_2^2}\) and \(r_2(x)=\sqrt{x_3^2+x_4^2}\) from the subspace \(\dot{H}_{(2,2)}^{1,3} (\mathbb R^4)\) of the Sobolev space \(\dot {H}^{1,3}(\mathbb R^4)\), radially symmetric in variables \((x_1, x_2)\) and in variables \((x_3,x_4)\): \[ \int_{\mathbb R^4}\frac{u^2}{r_1(x)r_2(x)}\mathrm{d}x \leq C\int_{\mathbb R^4}|\nabla u|^2 \mathrm{d}x, \] Similarly to the previously studied radial case, the range of parameters in CKN inequalities can be extended, sometimes to infinity, providing a pointwise estimate similar to the radial estimate in [W. A. Strauss, Commun. Math. Phys. 55, 149–162 (1977; Zbl 0356.35028)]. Furthermore, the “multi-radial” weights are a stronger singularity than radial weights of the same homogeneity, e.g. \(\frac{1}{r_1(x)r_2(x)}\geq \frac{1}{2| x|^2}\).