A well testing method and apparatus for reservoir characterization during a drilling operation by making use of conventional drilling facilities. The tests can be performed at various degrees of wellbore penetration in the formation. If the test is conducted as soon as the top of the formation is penetrated by the bit, the effects of formation damage (skin) may be minimized or even eliminated. The proposed technique is particularly suitable for formations displaying weak pore structure, tight formation, and/or relatively low reservoir pressure. The method consists of two major steps; a drawdown test with a variable rate, and a build up test. A computer simulator is necessary and also useful for pressure transient analysis for determination of reservoir pressure and transmissibility. From the data recorded from a single well test utilizing this method and apparatus, fluid mobility and formation thickness can be calculated.