Cell membrane tension plays a critical rule in a variety of cellular activities, including membrane protein signaling, cell motility and cell blebbing. The specific mechanical environment of eukaryotic cells may result the spatially dependent membrane tension, which is crucial to actin filaments activity. In this work, we will start with simple fluid model to estimate lipid membrane tension in terms of active contractile interaction of actin filaments and polymerization/depolymerization rate. We includes the case of suspended cells and lamellipodium-membrane tension at cells resting on 2D substrates. The simple mechanical model will give us an overall scene of membrane tension distribution at specific order of magnitude, including the surface tension gradient, which cannot be measured by conventional experiment. Membrane tension also actively controls cell membrane blebbing. We also discuss the case of cell motility. We purpose the jet propulsion is the main mechanism for cell moving. The fluid field around the cell imposes an unique mechanical environment to the cell, which we will further demonstrate surface tension distribution and membrane net flow due to the spatially variant tension.