Specific morphological features of polymer semiconductors are often promoted in devices to optimize optoelectronic behavior. Less studied is the role of morphology on the mechanical properties of the film, such as elastic modulus, which is an important property for the development of flexible and stretchable devices. To gain insight into the morphological origin of elasticity in polymer semiconductors and its relationship to charge transport, we study the anisotropic in-plane elastic modulus of strain-aligned regioregular poly(3-hexylthiophene) (P3HT) films and compare the results to previously measured field effect charge mobility. The film morphology is varied through the amount of applied strain and post strain thermal annealing. Morphological characterization includes UV-vis optical spectroscopy and X-ray diffraction. The elastic modulus is measured using a buckling-based measurement technique. The elastic modulus of the film is found to decrease as the film is plastically strained. Thermally annealing the strained films results in a large in-plane elastic modulus anisotropy, where the modulus increases in the direction of backbone alignment and decreases in the transverse direction. The measured elastic modulus is compared to the film morphology, showing a dependence on both in-plane polymer chain alignment and local aggregate order. Comparing the elastic modulus to field effect mobility shows that they are not necessarily correlated, which has important implication for flexible organic electronic device design.