Additive manufacturing techniques may be utilized to construct effusion plates. Such additive manufacturing techniques may include defining a configuration for an effusion plate having one or more internal cooling channels. The manufacturing techniques may further include depositing a powder into a chamber, applying an energy source to the deposited powder, and consolidating the powder into a cross-sectional shape corresponding to the defined configuration. Such methods may be implemented to construct an effusion plate having one or more channels with a curved cross-sectional geometry.