We present the design of a positron emission tomograph (PET) with flexible geometry dedicated to in vivo studies of small animals (TierPET). The scanner uses two pairs of detectors. Each detector consists of 400 small individual yttrium aluminum perovskite (YAP) scintillator crystals of dimensions 2 x 2 x 15 mm3, optically isolated and glued together, which are coupled to position-sensitive photomultiplier tubes (PSPMT's). The detector modules can be moved in a radial direction so that the detector-to-detector spacing can be varied. Special hardware has been built for coincidence detection, position detection, and real-time data acquisition, which is performed by a PC. The single-event data are transferred to workstations where the radioactivity distribution is reconstructed. The dimensions of the crystals and the detector layout are the result of extensive simulations which are described in this report, taking into account sensitivity, spatial resolution and additional parameters like parallax error or scatter effects. For the three-dimensional (3-D) reconstruction a genuine 3-D expectation-maximization (EM)-algorithm which can include the characteristics of the detector system has been implemented. The reconstruction software is flexible and matches the different detector configurations. The main advantage of the proposed animal PET scanner is its high flexibility, allowing the realization of various detector-system configurations. By changing the detector-to-detector spacing, the system is capable of either providing good spatial resolution or high sensitivity for dynamic studies of pharmacokinetics.