We first develop a new variant of Cannon’s algorithm for parallel matrix multiplication on rectangular process grids. Then we tailor it to selected situations where at least one triangular matrix is involved, namely “upper triangle of (full × upper triangular),” “lower triangle of (lower triangular × upper triangular),” and “all of (upper triangular × rectangular).” These operations arise in the transformation of generalized hermitian positive definite eigenproblems AX=BXΛ to standard form A˜X˜=X˜Λ, and making use of the triangular structure enables savings in arithmetic operations and communication. Numerical results show that the new implementations outperform previously available routines, and they are particularly effective if a whole sequence of generalized eigenproblems with the same matrix B must be solved, but they can also be competitive for the solution of a single generalized eigenproblem.