There are a large number of remedies in traditional medicine focused on relieving pain and inflammation. Flavanones have been a potential source in the search for leading compounds and biologically active components, and they have been the focus of much research and development in recent years. Eysenhardtia platycarpa is used in traditional medicine for the treatment of kidney diseases, bladder infections, and diabetes mellitus. Many compounds have been isolated from this plant, such as flavones, flavanones, phenolic compounds, triterpenoid acids, chalcones, sugars, and fatty acids, among others. In this paper, natural flavanone 1 (extracted from Eysenhardtia platycarpa) as lead compound and flavanones 1a–1d as its structural analogues were screened for anti-inflammatory activity using Molinspiration® and PASS Online in a computational study. The hydro alcoholic solutions (FS) of flavanones 1, 1a–1d (FS1, FS1a–FS1d) were also assayed to investigate their in vivo anti-inflammatory cutaneous effect using two experimental models, a rat ear edema induced by arachidonic acid (AA) and a mouse ear edema induced by 12-O-tetradecanoylphorbol acetate (TPA). Histological studies and analysis of pro-inflammatory cytokines TNF-α, IL-1β, and IL-6 were also assessed in AA-inflamed rat ear tissue. The results showed that the flavanone hydro alcoholic solutions (FS) caused edema inhibition in both evaluated models. This study suggests that the evaluated flavanones will be effective when used in the future in skin pathologies with inflammation, with the results showing 1b and 1d to be the best.