Theoretical soft matter physics analysis will be applied to study the physical properties of lamellipodia, thin flat extensions from cell body that grabs the substrate below. First, the steady state thickness of lamellipodia as a function of the density of actin polymerization activators on cell membrane, actin monomers in the cytoplasm, myosin contractility in the lamellipodia will be calculated. From this result we will calculate the response of lamellipodia under compression, this calculation can be used to compared to experimental studies of the physical properties of lamellipodia with AFM. The fluctuations of the thickness of lemellipodia in the steady will also be studied as it is an important observable for experiments conducted by optical microscopes. It is expected that this series of studies will much improve our understanding of the lamellipodia from a systematic, physical science point of view.