A semi-analytical model is presented to study transient pressure behaviour of vertical wells in a dual porosity reservoir under the influence of non-Darcy flow inside the reservoir (Forchheimer number), formation damage around the wellbore (mechanical skin factor), and their combined effect (near-wellbore non-Darcy skin factor). Unique transient pressure behaviour is presented in both semi-log pressure and log-log pressure derivative plots. Semi-log pressure plots suggest that for a vertical well producing with a constant sandface flow rate, its pressure responses exhibit two linear portions for Darcy now, even with non-Darcy skin factor (i.e. the near-wellbore non-Darcy skin factor is larger than zero). However, the first linear portion will dismiss if non-Darcy flow presents inside the reservoir (i.e. the Forchheimer number is larger than zero). Further pressure derivative analyses in a log-log Plot suggest that: 1) both Forchheimer number and near-wellbore non-Darcy skin factor lead to a narrower and steeper transition region between pure wellbore storage and radial flow region for build up tests and a wider and gentler one for draw-down tests; and 2) the derivative curves under the effect of the Forchheimer number always exhibit a slight convex shape in the radial flow region, rather than a horizontal line with a constant value of 0.5 for Darcy flow. The type curves presented may be applied to estimate mechanical skin factor, Forchheimer number and near-wellbore non-Darcy skin factor from a single rate test. Synthetic cases show that ignoring the globally distributed non-Darcy flow causes errors of up to 300% in interpreting dual porosity characteristic parameters. Both synthetic and field case studies suggest that the non-Darcy flow has a significant effect on the interpretation of the inter-porosity flow coefficient, lambda, and less effect on the interpretation of the storativity ratio, omega.