Aircraft landing gears are subjected to a wide range of excitation conditions, which result in conflicting damping requirements. A novel solution to this problem is to implement semi-active damping using magnetorheological (MR) fluids. This paper presents a design methodology that enables an MR landing gear to be optimized, both in terms of its damping and magnetic circuit performance, whilst adhering to stringent packaging constraints. Such constraints are vital in landing gear, if MR technology is to be considered as feasible in commercial applications. The design approach focuses on the impact or landing phase of an aircraft's flight, where large variations in sink speed, angle of attack and aircraft mass makes an MR device potentially very attractive. In this study, an equivalent MR model of an existing aircraft landing gear is developed. This includes a dynamic model of an MR shock strut, which accounts for the effects of fluid compressibility. This is important in impulsive loading applications such as landing gear, as fluid compression will reduce device controllability. Using the model, numerical impact simulations are performed to illustrate the performance of the optimized MR shock strut, and hence the effectiveness of the proposed design methodology. Part 2 of this contribution focuses on experimental validation.