Let 𝑛,𝑘 be positive integers such that 𝑛≥𝑘 and 𝐺 be a tripartite graph with parts 𝐴,𝐵,𝐶 such that ∣𝐴∣=∣𝐵∣=∣𝐶∣=𝑛. Denote the edge densities of 𝐺⁡[𝐴,𝐵],𝐺⁡[𝐴,𝐶] and 𝐺⁡[𝐵,𝐶] by 𝛼,𝛽 and 𝛾, respectively. In this paper, we study edge density conditions for the existence of 𝑘 vertex-disjoint triangles in a tripartite graph. For 𝑛≥5⁢𝑘+2 we give an optimal condition in terms of densities 𝛼,𝛽,𝛾 for the existence of 𝑘 vertex-disjoint triangles in 𝐺. We also give an optimal condition in terms of densities 𝛼,𝛽,𝛾 for the existence of a triangle-factor in 𝐺.