This thesis is devoted to study the dynamics of self-gravitating objects in scalar-tensor gravity. In this setting, we explore evolution of spherical, axial and cylindrical filamentary stellar systems in the framework of self-interacting Brans-Dicke gravity. We formulate a set of equations which govern the dynamics of evolving gravitating fluids through dynamical variables. We also calculate structure scalars by using orthogonal splitting of the Reimann tensor to make the analysis simple. In spherical case, we discuss some particular fluid models according to different dynamical conditions. It turns out that fluid models for regular distribution of scalar field are consistent with general relativity while models due to irregular distribution deviate. We determine inhomogeneity factors and find that inhomogeneity is a necessary condition for the resultant fluid models. We also explore static inhomogeneous anisotropic spherical solutions with the help of structure scalars. In static axially symmetric case, we discuss physically feasible sources of models and inhomogeneity factors of the system. It is found that structure scalars related to double dual of the Riemann tensor control the density inhomogeneity. We also obtain exact solutions of homogenous isotropic and inhomogeneous anisotropic spheroid models. It is concluded that homogenous models involve homogenous distribution of dark energy source (scalar field) whereas inhomogeneous correspond to inhomogeneous scalar field. Finally, we study dynamical instability of non-static axial reflection symmetric and cylindrically symmetric filamentary models in weak-field approximations. In axially reflection symmetric case, we formulate hydrodynamical equations and discuss oscillations using time-dependent perturbation for both spin as well as spin-independent cases. We discuss instability of oscillating models in Newtonian and post-Newtonian limits. It is found that the oscillations and stability of the model depend upon the dark energy source along with anisotropy and reflection effects. We conclude that x xi the axial reflection system remains stable for stiffness parameter Γ = 1, collapses for Γ > 1 and becomes unstable for 0 < Γ < 1. For cylindrically symmetric stellar filaments, we construct polytropic filamentary models through generalized Lane-Emden equation in Newtonian regime. The resulting models depend upon the values of cosmological constant (due to scalar field) along with polytropic index and represent a generalization of the corresponding models in general relativity.