Adhesively-bonded joints can have spatial variations in bondline thickness with respect to their overlap length. Assumptions pertaining to shear-lag and adherend transverse shear deformation are used to compose a governing differential equation that permits any mathematical function to be used for representing the variation in bondline thickness, t(a) (x). Finite Difference solution techniques are employed to solve this equation, and it is shown by a series of case study example calculations that the adhesive shear stress changes significantly for deviations about a baseline, uniform thickness, configuration. It is also shown that for cases when the gradient in bondline thickness is small, simple closed-form solutions developed strictly for uniform thickness joints can provide reasonable accuracy. Numerical results are summarized as "stress concentration factor" curves, allowing quick estimation of the upper and lower bounds of normalized peak shear stress in joints having varying degrees of thickness imperfection.