I wonder what is criteria for this test, which reasons important when design transformer for this test? Axial, radial forces or distance between low voltage and high voltage coils or other things?
The meaning of the short circuit proof design of a transformer is easy to understand: in case a short circuit happens in your grid and the damages are repaired, you don't really like to find after you switch on the power again that your transformer fails after short time.
IEEE C57.12.90 and IEC 60076-5 give the requirements and procedure for the short circuit test but all transformers need to be designed and manufactured to withstand the thermal and dynamic effects of external short circuits whether they will be tested or not. You should not be designing any differently just because a particular transformer design is going to be tested. Both the above standards give the method to calculate the temperature rise during short circuit note that this temperature rise does not occur and is not measured during the test. Thermal capability is rarely an issue for power transformers due to their (usually) higher impedance. Dynamic effects fall broadly into radial and axial forces/stresses. Radial forces/stresses can usually be calculated quite easily by 'pencil and paper' but axial forces and the resulting stresses require a detail knowledge of the magnetic field within the windings. Once the forces/stresses are known they need to compare.
To the manufacturers well established design rules ideally backed up by test evidence on other transformers or models. IEC 60076-5 does give some suggested values in Annex A for some of the key stresses based on industry practice and experience. Manufacturers can propose higher values if they have good experience with previously tested transformers. The short circuit test is the ultimate proof of the manufacturers design rules and manufacturing practices.