A tensioned tent structure (10) includes a flexible covering (20) having a vertex portion (22) and spaced corner portions (24) and which has a selected geometrical shape in the erect position. The tent structure further includes an anchor (70) for securing each corner portion (24) to the support surface (12) and a pole assembly (100) that supports the covering (20) in an erect state with the vertex (22) above the support surface (12). The pole assembly has an extension and contraction mechanism (102) to vary its effective length to apply upward force to the vertex portion thus tensioning the covering to draw it taut. The broad method of the present invention thus contemplates the broad steps of providing such a flexible covering (20) having a vertex (22) and corner portions (24), securing the corner portions (24) to the support surface (12), positioning a pole assembly (100) in an upright position between the support surface (12) and the vertex portion (22) and forcibly expanding the pole assembly to tension the flexible covering in a taut condition. Preferably, the tent structure has a base perimeter in the shape of a regular polygon with the structure shaped generally as a pyramid. The covering (20) is formed of fabric panels (36),(38) cut to enhance the effect of tensioning forces. The invention also contemplates tent structures having a plurality of center pole assemblies.