Soil compaction of arable land, caused by heavy machinery constitutes a major threat to agricultural soils in industrialized countries. The degradation of soil structure due to compaction leads to decreased (macro-) porosity resulting in increased mechanical impedance, which adversely affects root growth and crop productivity. New crop cultivars, with root systems that are adapted to conditions of increased soil strength, are needed to overcome the limiting effects of soil compaction on plant growth. This study aimed (i) to quantify the genetic diversity of early root system development in wheat and to relate this to shoot development under different soil bulk densities and (ii) to test whether root numbers are suitable traits to assess the genotypic tolerance to soil compaction. Fourteen wheat genotypes were grown for 3 weeks in a growth chamber under low (1.3 g cm-3), moderate (1.45 g cm-3), and high soil bulk density (1.6 g cm-3). Using X-ray computed tomography root system development was quantified in weekly intervals, which was complemented by weekly measurements of plant height. The development of the root system, quantified via the number of axial and lateral roots was strongly correlated (0.78 < r < 0.88, p < 0.01) to the development of plant height. Furthermore, significant effects (p < 0.01) of the genotype on root system development and plant vigor traits were observed. Under moderate soil strength final axial and lateral root numbers were significantly correlated (0.57 < r < 0.84, p < 0.05) to shoot dry weight. Furthermore, broad-sense heritability of axial and lateral root number was higher than 50% and comparable to values calculated for shoot traits. Our results showed that there is genetic diversity in wheat with respect to root system responses to increased soil strength and that root numbers are suitable indicators to explain the responses and the tolerance to such conditions. Since root numbers are heritable and can be assessed at high throughput rates under laboratory and field conditions, root number is considered a promising trait for screening toward compaction tolerant varieties.