This paper presents a static-equilibrium oriented interaction force modeling and control approach of aerial manipulation employing uni-directional thrust (UDT) multirotors interacting with variously defined environments. First, a simplified system model for a quadrotor-based aerial manipulator is introduced considering parameterized work surfaces under assumptions, and then a range of meaningful manipulation tasks are utilized to explore the system properties in a quasi-static equilibrium state. An explicit interaction force model in relation with the aerial manipulator pose configuration and the environment parameter is derived from the static equilibrium analysis, based on which singularity is pointed out. Then a hybrid attitude/force interaction control strategy is presented to verify the proposed interaction force model, which involves high gain attitude control and feedforward plus feedback force control. This paper represents preliminary results. We study the properties of UDT-based aerial manipulators via specific tasks, and propose a novel framework for interaction force modeling and control aiming at maximizing the commercial values of UDT platforms for aerial manipulation purpose.