This study explores the role of rate and biases of technological change in the sustainability of an economy with an exhaustible resource. In order to achieve this goal, the mathematical concept of viability kernel is introduced as a sustainability indicator and necessary conditions for sustainability are completely depicted in terms of technological parameters. The literature has historically assumed substitutability between human capital and natural resources and technological progress that is neutral in terms of relative input productivity and minimum efficient scale of production. Both assumptions have been widely criticized given the patterns of technological change and substitution observed empirically. Hence the theoretical contribution developed here allows calculation of sustainability thresholds in a manner that permits two of the most important drivers of economic behavior, substitution possibilities and biased technical change. As a result, necessary conditions for sustainability are derived in terms of rate and bias of technical change and elasticity of substitution. Results previously derived in the literature are reviewed and comparisons are made with new results derived from more flexible technological specifications. Several important results are found. First, the identification between elasticity of substitution and sustainability breaks down. Second, a rather optimistic result is obtained by which Increasing Returns to Scale sometimes can prevent the economy from extinction even with zero technological progress and positive capital depreciation. Third, input bias of technical change is critical in determining sustainability and further, size-increasing bias of technical change increases the likelihood of an economy to be sustainable in all cases.