After studying at Pražská technika in Prague, he worked in the studio of Jan Kotěra in 1917-18, becoming an official of the State Monument Care. From 1923 he was an independent designer. He was also an editor and author for many architectural magazines (mostly Stavba, Stavitel and Architekt SIA). In the 1920s, he focused mainly on the design of residential buildings, like typed family houses built for some colonies in South-western Ukraine (1918-38 part of Czechoslovakia), apartment buildings in Ostrava, Pilsen, Prague and public buildings. In 1931, he won the Včela workers' association competition for tenement houses with small flats. Probably the most famous building is the architect's own villa in the street Nad Santoškou 1 in Prague, mentioned in period magazines as an example of modern architecture. In addition, Říha devoted himself to the installation of dozens of exhibitions, including state expositions of pre-war Czechoslovakia abroad. It is also worth mentioning that in his studio in 1927 the young Karel Honzík occasionally helped out.
Around 1930, the architect Říha also began to address issues of urban, territorial and landscape planning. Říha and Otokar Fierlinger commissioned the Institute for Urban Development at the Masaryk Academy to prepare in 1932 the text "The City and the Adjustment Plan" (Město a upravovací plán). They created a brief overview of the methodology and contemporary technique of regulatory plans, urban planning and their surroundings, and the promise of regional plans. Chapters on recreation, green areas and the protection of natural monuments are no longer missing.
In the second half of the 1930s, Říha focused even more on the issues of rural development, village and regional planning.
In 1948 he published the unique book "The Beautiful Land: A Book on Nature, Civilization and Planning" (Země krásná: kniha o přírodě, civilisaci a plánování). The book is actually an introduction to landscape planning, it deals with historical contexts, geology, largely botany and geobotany, technical development, but also garden and park architecture, urban planning, spatial planning, aesthetic and ethical values of nature and nature conservation.
Only a few projects are known from the post-war work, e. g. Prague-Motol crematorium (1951-54). Probably the architect's last major project was the study of recreation in the Beroun region in the mid-1960s. Říha did not receive official honors until the end of the 1960s, when he was re-admitted to the Association of Architects (Svazu architektů) and awarded on the occasion of the 50th anniversary of the founding of the Czechoslovak Republic.