In the present study, dynamic response of single-cylinder reciprocating engines is investigated. The models examined take into account the flexibility of the engine mechanism associated with either its connecting rod or its supporting bearings. In addition, both the driving and the resisting moments are expressed as functions of the crankshaft motion. This leads to dynamic models with equations of motion appearing in a strongly nonlinear form. These equations are then solved numerically, by employing methodologies of both the time and the frequency domain. In particular, these methodologies include determination of transient response by direct integration or direct determination of complete branches of steady state response. The first set of numerical results refers to engine mechanisms with a flexible connecting rod. After dealing briefly with the special case of constant crank angular velocity, which can be investigated more easily and provides valuable insight into some aspects of the system dynamics, the emphasis is shifted to the general case of non-ideal forcing. Next, numerical results are presented for engine models with flexible bearings. Initially, mechanisms with rigid members supported by bearings involving linear anisotropic or isotropic properties are considered. Finally, similar results are also presented for hydrodynamic bearings, whose behavior is governed by the classical finite-length impedance theory. In all cases, the attention is focused on investigating the influence of the system parameters on its dynamics.