Polymeric, soft, and biological materials exhibit viscoelasticity, which is a time dependent mechanical response to deformation. Material viscoelasticity emerges from the movement of a material’s constituent molecules at the nano- and microscale in response to applied deformation, and viscoelastic properties therefore depend on the speed at which a material is deformed. Recent technological advances, especially in atomic force microscopy (AFM), have provided tools to measure and map material viscoelasticity with nanoscale resolution. However, to understand more about the viscoelastic behavior of a material from such measurements, theoretical grounding during data analysis is required. For example, commercially available bimodal AFM imaging maps two different viscoelastic properties of a sample, the storage modulus, E′, and loss tangent, tanδ, with each property being measured by a different resonance frequency of the AFM cantilever. While such techniques provide high resolution maps of E′ and tanδ, the different measurement frequencies make it difficult to calculate key viscoelastic properties of the sample such as: the model of viscoelasticity that describes the sample, the loss modulus, E′′, at either frequency, elasticity E, viscosity η, and characteristic response times τ. To overcome this difficulty, we present a new data analysis procedure derived from linear viscoelasticity theory. This method is applied and validated by performing amplitude modulation-frequency modulation (AM-FM) AFM, a commercially available bimodal imaging technique, on a styrene-butadiene rubber (SBR) with known mechanical behavior. The new analysis procedure correctly identified the type of viscoelasticity exhibited by the SBR and accurately calculated SBR E, η, and τ, providing a useful means of enhancing the amount of information gained about a sample’s nanoscale viscoelastic properties from bimodal AFM measurements. Additionally, being derived from fundamental models of linear viscoelasticity, the method can be employed for any technique where different viscoelastic properties are measured at different and discrete frequencies with applied deformations in the linear viscoelastic regime of a sample.