Summary Since seismic modeling is conducted repeatedly in seismic inversion, efficiency and accuracy of inversion are affected by seismic modeling algorithm used in it. One of the main factors influencing accuracy of seismic modeling can be the boundary condition used to remove edge reflections arising from finite-size models. For elastic modeling and inversion algorithms free from edge reflections, we propose using the logarithmic grid set. In the logarithmic grid set, the origin is located in the middle of surface of a given model and grid interval increases logarithmically with distance from the origin. The logarithmic grid set enables us to incorporate huge boundary areas with fewer grid points than in the conventional grid set, so that edge reflections are not recorded within the recording duration. For elastic modeling and inversion in the logarithmic grid set, wave equations and source position are first transformed to the logarithm-scaled coordintate. To convert field data from the conventional grid set to the logarithmic grid set and transform inversion results from the logarithmic grid set to the conventional grid set, interpolation algorithms are needed. In the elastic modeling algorithm, the cell-based finite-difference method, which properly describes the free-surface boundary conditions, is used. For inversion process, we apply the gradient method based on the back-propagation method, the pseudo-Hessian matrix, and the conjugate-gradient method. We also employ the frequency-marching method. Numerical examples generated for the modified version of the Marmousi-2 model showed that the elastic modeling and inversion algorithms designed in the logarithmic grid set yield reasonable results.