In a level directed acyclic graph G = (V;E) the vertex set V is partitioned into k ≤ |V | levels V ¹; V ²... V ^k such that for each edge (u, v) ∈ E with u ∈ V ⁱ and v ∈; V ^j we have i < j. The level planarity testing problem is to decide if G can be drawn in the plane such that for each level V ⁱ, all v ∈ V ⁱ are drawn on the line l _i = {(x, k - i) | x ∈ ℝ}, the edges are drawn monotonically with respect to the vertical direction, and no edges intersect except at their end vertices. In order to draw a level planar graph without edge crossings, a level planar embedding of the level graph has to be computed. Level planar embeddings are characterized by linear orderings of the vertices in each V ⁱ (1 ≤ i ≤ k). We present an O(|V |) time algorithm for embedding level planar graphs. This approach is based on a level planarity test by Jünger, Leipert, and Mutzel [6].