Additively-manufactured (AM) materials have a defined mesostructure and natural voids which impact their structural stability; thin shells which so not have bulk to support or absorb the effects of the variances in properties are particularly affected. Thin shells are a common feature in many designs, providing good strength-to-weight ratios for many applications, particularly in the aerospace and structural design domains. The use of AM processes to produce thin structures could both expand the use of AM and improve the application space for thin structures in design, but this problem has not yet been widely explored for buckling cases. The brief exploratory study presented in this paper examined the characteristics and critical buckling load of thin-walled ABS and PLA cylinders under static axial and angled radial loading. A designed 2(4-1) factorial experiment was used to explore the buckling behavior, examining the impact of wall thickness, material, and two kinds of internal reinforcement (soft infill and polyurethane foam). Analysis of variance (ANOVA) (including model adequacy testing and proof of Fisher Assumption validity) was completed on data from two replications (32 total tests), providing useful information on the significance of the factors and their interactions. The data is provided in full, along with a discussion of the experimental design and testing method, the results, and the importance of this problem in further research efforts. The results of the tests showed a dramatic variance in the performance based on the characteristics of the cylinders. The data collected can be used to drive future work toward the modeling and design of hard polymer AM thin structures, as well as developing efficient and low-cost methods for testing and exploring these structures for practical design problems.