This paper presents mathematical solutions for well tests in heterogeneous and bounded formations. Several dozen cases are considered, and methods for developing Laplace solutions for these cases are proposed. Many of the solutions are presented, including the following cases: a. an arbitrarily placed well in a three-composite concentric system, b. an arbitrarily placed well in a two-composite concentric system, c. solutions for two-well configurations including interference in composite systems, and d. a specific section with solutions near composite linear discontinuities. Four types of active wells are considered: a line-source constant-rate well, a finite-radius constant-rate well with storage and skin, a slut-test well with storage and skin, and a constant-pressure well. Active wells and interference wells are placed arbitrarily within the domains for most configurations presented in this paper. In addition, boundary skins between regions are introduced as a means of simulating faults or boundaries between fluid banks. The paper ends with examples showing how the wellbore responses depend upon the interaction of various reservoir and well parameters.