Stream-wise velocity-gradients associated with extensional flows arise in thinning liquid necks spontaneously formed during jetting, printing, coating, spraying, atomization, and microfluidic-based drop formation. In this contribution, we employ Dripping-onto-Substrate (DoS) rheometry protocols to measure the extensional rheology response of intrinsically semi-dilute polymer solutions by visualizing and analyzing capillary-driven thinning of a columnar neck formed between a nozzle and a sessile drop. We show that extensional viscosity that quantifies the resistance to stream-wise velocity gradients is orders of magnitude higher than the shear viscosity. Although shear flows only weakly perturb the chain dimensions, extensional flows can strongly stretch and orient the chains, thus influencing both intra-and inter-chain interactions. We find that the extensional relaxation times for intrinsically semi-dilute PEO solutions in a good solvent for five different molecular weights increase linearly with concentration, exhibiting a stronger concentration dependence than observed for dilute solutions, or anticipated by blob models, developed for relaxation of weakly perturbed chains in a good solvent. The observed distinction between the concentration-dependent relaxation dynamics of intrinsically dilute and semi-dilute solutions arises due the complex influence of stretching, conformational anisotropy, and polymer concentration on excluded volume and hydrodynamic interactions of flexible, highly extensible polymers. (C) 2017 Wiley Periodicals, Inc.