Often and for many reasons the wellbore does not completely penetrate the entire formation, yielding a unique early-time pressure behaviour. Some of the main reasons for partial penetration, in both fractured and unfractured formations, are to prevent or delay the intrusion of unwanted fluids into the wellbore, i.e., water coning. The transient flow behaviour in these types of completions is different and more complex compared to that of a fully penetrating well. This paper proposes a method for identifying, on the pressure and pressure derivative curves, the unique characteristics of the different flow regimes resulting from these types of completions and to obtain various reservoir parameters, such as vertical and horizontal permeability, fracture properties and various skin factors. Both naturally fractured and unfractured (homogeneous) reservoirs have been investigated. For a naturally fractured formation, the type curves of the pressure and pressure derivative reveal that the combination of partial penetration and dual-porosity effects yields unique finger prints at early and transition periods. These unique characteristics are used to calculate several reservoir parameters, including the storage capacity ratio, interporosity flow coefficient, permeability and pseudoskin. Equations have been developed for calculating the skin for three partial completion cases: top, centre and bottom. The analytical solution was obtained by combining the partially penetrating well model in a homogeneous reservoir with the pseudo-steady model for a naturally fractured reservoir (NFR). The interpretation of pressure tests is performed using the TDS (Tiab's Direct Synthesis) technique for analyzing log-log pressure and pressure derivative plots. The TDS technique uses analytical equations to determine reservoir and well characteristics without using type-curve matching. These characteristics are obtained from unique fingerprints, such as flow regime lines and points of intersection of these lines, which are found on the log-log plot of pressure and pressure derivative. Two numerical examples are included to illustrate the application of the proposed technique.