In normal practice, ease in processing comes at the expense of a reduction in mechanical properties. Here we show that by controlled synthesis it is possible to synthesize a wide range of linear ultrahigh-molecular-weight polyethylenes that can be stretched uniaxially into tapes. In these uniaxially drawn tapes, the bundles of fibers align themselves in a preferred crystal plane orientation, accounting for an extraordinarily high tensile modulus. The stretching process is accomplished in the solid state with no need for any solvent. The ease of solid-state processing provides a unique opportunity to follow the influence of the molar mass on the tensile properties. The uniaxially drawn tapes, similar to the fibers spun from solvent, confirm the empirical relationship between tensile strength and tensile modulus proposed by van Krevelen in 1976 and subsequently supported by experimental findings on solution-spun fibers by Smith and Lemstra. However, the solid-state-processed tapes do not achieve the high values of tensile strength expected from this relationship, where a modulus of 200 GPa would correspond to a tensile strength of 5 GPa. The relatively lower tensile strength of 4 GPa for the extraordinarily high modulus of 200 GPa observed in the uniaxially stretched tapes is attributed to the presence of defects, as tapes can be considered composites of fibers. The high modulus in combination with the tensile strength in tapes has the potential to provide unique physical properties in composites.