We design and fabricate an apparatus which uses two dual double cantilever flexures to probe mechanical properties of self-assembled monolayers (SAM) under compression. The cantilevers were designed to give stiffness of the same order as the SAM. One of the cantilevers carrying the probe is vibrated sinusoidally at subresonance frequency and subnanometric amplitude while the dynamic response of the other carrying the SAM is recorded in the contact mode to yield data which could be deconvoluted to give stiffness and damping constant of the SAM under compression using a model of viscoelasticity. We validate the apparatus as well as the method of deconvolution by indenting bulk polytetrafluoroethylene and estimate mechanical properties of SAMs of different chain length and head group. The approach adopted here is able to distinguish in terms of mechanical properties a bulk polymer from a SAM and also between two SAMs of similar but subtly different structure.