Acid fracturing has been widely used as an industry practice in explored and developed carbonate reservoirs. It is very important to understand responses of reservoirs and improve production performance of a well due to the presence of fracture networks by stimulation treatments. Pressure transient analysis is one of the most effective diagnostic techniques available to enhance our understanding of natural and artificial-etched fracture behavior. This work presented a novel mathematical model for unsteady state flow of naturally fractured porous medium into multiple etched fractures intersecting a vertical well, and three different geometric shapes of matrix blocks containing slabs, cylinders and spheres were considered. The new solution was derived by using the Laplace transformation and the point source function integral approach. The polar coordinate transformation was used to deal with the radial distribution of arbitrary fracture number and angle. Then the model was validated by comparison with three published cases. Finally, type curves were plotted to identify flow regimes: linear flow, transitional flow, pseudoradial flow, and boundary dominant flow if the closed or constant pressure boundary exists. Furthermore, sensitivity analysis was investigated. The results showed that the acid-etched fracture parameters containing fracture number, fracture distribution and conductivity had a significant impact on pressure behavior at early times. However, natural fracture storativity coefficient and interporosity flow parameter mainly affected the transitional flow at intermediate times. Moreover, the shape of matrix blocks had a little influence on transient responses at intermediate times. It is found that multiple etched fractures existing near the wellbore consume less pressure drop and increase the productivity of a well as a whole.