Many reinforced concrete shear wall buildings subjected to the Mw 8.8 2010 Chile earthquake suffered no damage even though they were subjected to seismic demands significantly larger than the design strength. Analytical studies previously conducted by the authors on undamaged buildings, however, showed that linearly elastic demands due to ground motions recorded during the 2010 Chile earthquake exceed the capacity of many walls. This dichotomy between empirical evidence and results given by linear analysis highlights the need for non-linear analysis to accurately assess the strength of wall buildings. In this paper, an actual wall building not damaged by the 2010 Chile earthquake is analyzed with non-linear techniques to assess the amount of overstrength and to evaluate the response to the 2010 Chile earthquake. Non-linear pushover and time history analyses were performed. Results given by pushover analysis indicate large values of overstrength (greater than 3.4) that are very sensitive to the shear stiffness of the walls and to soil-structure interaction, but not to other modeling issues. The global response of the building is essentially unaffected by damage up to a roof drift ratio roughly equal to 0.004, which is similar to the roof displacement demand imposed by the recorded ground motions. When the rigid body rotation is accounted for, interstory drift ratios obtained from time history analysis are smaller than immediate occupancy limits, which is consistent with the actual lack of damage. It is then concluded that non-linear analysis is indeed necessary to realistically analyze the response of reinforced concrete shear wall buildings subjected to large seismic demands, even of those that remained undamaged.