In this paper soil-structure interaction (SSI) effects are investigated while an array of Pressurized Tuned Liquid Column Dampers (PTLCD) is employed for seismic vibration control of buildings. This device represents the most general case of a passive damper, with different reduction options to other control devices obtained by simplifying the involved parameters. Soil conditions considerably affect the control device functioning, because dynamic parameters such as natural frequency, damping factor, and natural modes depend on the soil properties. A simplified mathematical model is developed for the building with multiple degrees of freedom connected to a flexible base. For the time-domain analysis, a computational routine is developed for the linearization of the equilibrium equations of the PTLCD, as well as details for the reduction to the other types of passive dampers. Several numerical examples are selected for the analysis of the damper efficiency in reducing seismic vibration considering SSI. These simulations include Kobe earthquake data, which is applied to the model to evaluate the device performance under different scenarios. It is verified the influence of SSI in the natural frequency and structural response, which is related to the earthquake frequency components. Results confirm that the array of PTLCD's can reduce the vibration amplitudes, being more effective for soils with higher stiffness values.