This paper studies information freshness in information update systems operated with TDMA and FDMA. Information freshness is characterized by a recently introduced metric, age of information (AoI), defined as the time elapsed since the generation of the last successfully received update. In an update system with multiple users sharing the same wireless channel to send updates to a common receiver, how to divide the channel among users affects information freshness. We investigate the AoI performances of two fundamental multiple access schemes, TDMA and FDMA. We first derive the time-averaged AoI by estimating the packet error rate of short update packets based on Gallager's random coding bound. For time-critical systems, we further define a new AoI metric, termed bounded AoI, which corresponds to an AoI threshold for the instantaneous AoI. Specifically, the instantaneous AoI is below the bounded AoI a large percentage of the time. We give a theoretical upper bound for bounded AoI. Our simulation results are consistent with our theoretical analysis. Although TDMA outperforms FDMA in terms of average AoI, FDMA is more robust against varying channel conditions since it gives a more stable bounded AoI across different received powers. Overall, our findings give insight to the design of practical multiple access systems with AoI requirements.