In a tokamak the attainable β-values are restricted by the limitations of MHD-stability. The necessary improvement of the β-value should, however, be possible by going over to a non-circular plasma cross-section. In this paper, the theoretical conditions for such an improvement are discussed (e.g. volume currents peaked on axis, flattened ends of the elongated cross-section and diamagnetic plasma). Experimental investigations of this problem have been carried out in the Belt Pinch, where plasma production and heating is achieved by fast magnetic compression. This heating method is unusual for a tokamak, but is, at present, the only method of approaching the interesting β-regime (<β> ≈ 10 – 50%) and, especially, βpol > 1 operation.The main result of the Belt Pinch experiments is that MHD-stability requires about the same qcrit-value (≈ 3) also needed in circular-cross-section tokamaks, at least for the present plasma parameters and time scale (b/a ≈ 10, R/a ≈ 7, <β> ≈ 50%, <βpol> ≈5, Te ≈Ti ≈ 25 – 40 eV, <ne> ≈ 5 – 7 × 1014 cm−3, values approximately constant for the high-β-phase of 50 μs). Violation of q-condition, however, results in fast-growing modes which destroy the plasma equilibrium within several μs. Compared with such an unstable case, stability for t ≈ 50 μs means stable behaviour for about 20 MHD-growth-times. Numerical calculations indicate a further improvement in present and future experiments with suonger shock-heating and increased temperatures (T > 100 eV).