The response of multi‐degree‐of‐freedom (MDOF) structures with sliding supports is studied. The problem of sliding structures is a discontinuous one in that different numbers of equations of motion with varying forcing functions are required for the sliding and non‐sliding phases. The numerical difficulties involved in this regard in an incremental finite element analysis can be circumvented through the introduction of a fictitious spring for the sliding support. Such a treatment enables one to study the higher mode effects on MDOF sliding structures under the excitation of harmonic or earthquake motions. The dynamic characteristics of MDOF sliding structures will be highlighted in the analysis of a four‐storey shear building with sliding support.