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It is well known that torsionally unbalanced buildings are more vulnerable to earthquakehazards than are the regular structural systems. In this paper, a parametric investigation is presented, inorder to observe the amplification in the internal forces, when increased eccentricities are used instead ofthe ones corresponding to the 5% accidental eccentricity. A series of five, ten-story framed and walledstructures, with rather high torsional irregularity coefficients, are selected and a numerical test procedure isapplied. Numerical results show that the maximum amplification in the internal forces at the most criticalbeams and columns at the flexible sides of the structures is about 10%. It is concluded that, more seriousmeasures in the codes are needed in the case of this rather dangerous type of irregularity.